Hemlata

Analysis and mathematical model generation for letter frequencies in text and in words initials for Hindi language and measurement of entropies of most frequent consonants

Hemlata Pande,

Dept. of Mathematics,

University of Kumaun, S. S. J. Campus,

Almora, Uttarakhand (INDIA)

Email: [email protected]

H. S. Dhami,

Dept. of Mathematics,

University of Kumaun, S. S. J. Campus,

Almora, Uttarakhand (INDIA)

Email: [email protected]

1. Introduction

Linguistics is the scientific study of language. It endeavours to answer the question-what is language and how is represented in the mind? Its aim is to be able to characterize and explain the multitude of linguistic observations circling around us, in conversation, writing and other media. The underlying goal of the linguist is to try to discover the universals concerning language. That is, what are the common elements of all languages? The linguist then tries to place these elements in a theoretical framework that could describe all languages and could also predict what can not occur in a language. The properties of linguistic elements and their interrelations abide by universal laws which are formulated in a strict mathematical way, in analogy to the laws of well known natural sciences and it leads to the application of some abstract mathematical and statistical tools to the language theory. The term mathematical linguistics denotes a rather narrowly circumscribed set of issues including automata theory, set theory, and lambda calculus, with maybe a little formal language theory thrown in. It offers a number of tools that allow abstract theories of language and mental computation to be compared and contrasted with one another. An account of work in the field of mathematical methods of linguistics can be had from the book of Partee et al (1990), while compendium of several rules proposed to understand the linguistic structure by which language communicates can be seen in the work of Manning and Schutze (1999). One of the branches of mathematical linguistics is quantitative linguistics. It studies language by means of determining the frequencies of various words, word combinations, and constructions in texts. Currently, quantitative linguistics mainly means statistical linguistics. It provides the methods of making decisions in text processing on the base of previously gathered statistics. Statistical techniques have brought significant advances in broad-coverage language processing.

Zipfs ideas are the foundation stones of modern quantitative linguistics. His influence is not only restricted to linguistics but also incessantly penetrates other sciences as mentioned by Gabriel Altmann (2002). Zipf has ranked words with respect to their frequency of occurrence in order to find a relation between the frequency of occurrence of a word and its rank. Consequently this rank frequency approach was applied to different other components (than word) of language also. In this context we can cite the works of Sigurd, for suggesting a geometric series equation for the distribution of phoneme frequencies and of Good, for suggesting equation to describe the ranked distribution of phoneme and grapheme frequency, as given in the research paper of Yuri Tambovtsev and Colin Martindale (2007); Peter Grzybek and Emmerich Kelih (2005) for discussing a possible theoretical model for grapheme frequencies of Slavic alphabet and then suggesting that the negative hypergeometric distribution is as an adequate model; Ali Eftekhari (2006) for using Zipfs idea for introducing two new concepts Zipfs dimension and Zipfs order of letters in order to have a fractal geometrical approach for English texts; Yuri Tambovtsev and Colin Martindale (2007) for propounding that Yule equation fits the distribution of phoneme frequencies better than other distributions as Zipf, Good etc. The process of formation of language models is quite popular in linguistics. A linguistic model is a system of data (features, types, structures, levels, etc.) and rules, which, taken together, can exhibit a behavior similar to that of the human brain in understanding and producing speech and texts. Mathematical models for languages had been proposed by Harris (1982) in his famous book entitled A Grammar of English on Mathematical Principles. In statistical language modeling, large amounts of text are used to automatically determine the models parameters. A compendium of different statistical models can be seen in the book of Manning and Schutez (1999). Naranan and Balasubrahmanyan (1998) have described the use of power law relations in modeling of languages. A parsing language model incorporating multiple knowledge sources that is based upon the concept of constraint Dependency Grammars is presented in the paper of Wang and Harper (2002). A neural probabilistic language model has been generated by Bengio et al (2003) while hierarchical probabilistic neural network language model has been generated by Morin and Bengio (2005).Different neural network language models can be seen in the work of Bengio (2008).

The frequency of letters in text has often been studied for use in cryptography and frequency analysis. Modern International Morse code encodes the most frequent letters with the shortest symbols and a similar idea has been used in modern data-compression techniques also. Linotype machines are also based on letter frequencies of English language texts. The reference for these applications can be had from Nation Master- Encyclopedia (Letter frequencies).

Since the patterns of letters in language dont happen at random, so letter frequencies can be represented in the form of some rules and the pattern of letter frequencies can help in discrimination of random text from that of natural language text. According to Sanderson, R. (2007) distribution of letters in a text can potentially help in the process of language determination. We have tried to discuss the patterns of Hindi language alphabets on the basis of their occurrence in texts and as word initials with the application of the rank frequency approach.

2. Occurrence of letters in a text

We have initiated our work by counting the occurrence of letters of Hindi language alphabet in the text Tanav se mukti of author Shivanand (source has been given in appendix).Following aspects have been considered in the counting process:

Independent occurrence of each letter (vowel as well as consonant), as the occurrences of and in .

Each occurrence of consonants followed either by a vowel mark in Devanagari script written as matra, as occurrence of in , , , or occurrence in the form of half letters anywhere in the word. For example we may cite the example of occurrence of in and as such = + + + + + + + contains 2 , 1 , 1 and 1 and ( ++ + ++ +) contains four letters , , , once each.

Occurrence of has been considered as the occurrence of and of , , etc. with , etc. Occurrences in the form of , etc. have been merged with the occurrences of , and so on.

In our selected text Tanav se mukti the total counted values of the frequency of occurrence of each letter have been depicted in the following table 2.1:

Table 2.1

Letter

Frequency

Letter

Frequency

Letter

Frequency

Letter

Frequency

711

4468

92

4116

517

341

316

1128

99

679

3120

1850

167

122

543

589

458

0

1260

361

17

661

490

2645

449

194

3236

3178

23

848

1858

125

54

117

84

143

322

3

716

25

16

294

805

0

128

1921

Total

41,114

2

270

1553

If we represent the total occurrence of all the letters of alphabet in the text by N1, that is,

k=1, 2.. ,

be the frequency of occurrence of kth letter of the alphabet of Hindi language, then its value for the selected text shall be equal to 41,114.

_1295031832.unknown

_1295031855.unknown

We have ranked the letters in descending order of their frequency of occurrence as done by Zipf. The rank and frequency profile for each letter can be visualized as shown in the following table 2.2-

Table 2.2

Rank

Frequency

Rank

Frequency

Rank

Frequency

Rank

Frequency

Rank

Frequency

1

4468

11

1260

21

517

31

194

41

54

2

4116

12

1128

22

490

32

167

42

25

3

3236

13

848

23

458

33

143

43

23

4

3178

14

805

24

449

34

128

44

17

5

3120

15

716

25

361

35

125

45

16

6

2645

16

711

26

341

36

122

46

3

7

1921

17

679

27

322

37

117

47

2

8

1858

18

661

28

316

38

99

9

1850

19

589

29

294

39

92

10

1553

20

543

30

270

40

84

According to A. Eftekhari (2006) if the letters are ordered in accordance with their frequency of occurrence, the monotonic changes can be obtained by the application of the Zipfs law. Such type of arrangement has been given the name Zipfs order. For our text Tanav se Mukti the Zipfs order for occurrence of letters fin the text has been obtained as shown in the following figure-

3.Occurrence of letters as words initials

Results obtained by counting of letters for their occurrence as the beginning letters of words in the studied text have been tabulated in the following table 3.1.

_1296627712.xls

Chart1

0.0000486452

0.0000729678

0.000389162

0.000413484

0.00055942

0.000608065

0.001313421

0.0020431

0.002237681

0.002407939

0.002845746

0.002967359

0.003040327

0.003113295

0.003478134

0.004061877

0.004718587

0.006567106

0.007150849

0.007685946

0.007831882

0.008294012

0.008780464

0.010920854

0.011139758

0.011918081

0.012574792

0.01320718

0.01432602

0.016077249

0.016515056

0.017293379

0.017414992

0.019579705

0.020625578

0.02743591

0.030646495

0.037773021

0.044996838

0.045191419

0.046723744

0.064333317

0.075886559

0.077297271

0.078707983

0.100111884

0.108673445

Zipf's order of letters in the text(i)

Proportion of letters

Sheet1

4.86E-05

7.30E-05

0.000389162

0.000413484

0.00055942

K0.000608065

0.001313421

0.0020431

0.002237681

0.002407939

0.002845746

0.002967359

{k0.003040327

0.003113295

=0.003478134

0.004061877

0.004718587

0.006567106

0.007150849

0.007685946

0.007831882

0.008294012

0.008780464

0.010920854

0.011139758

0.011918081

0.012574792

0.01320718

0.01432602

0.016077249

0.016515056

0.017293379

0.017414992

0.019579705

0.020625578

0.02743591

0.030646495

0.037773021

0.044996838

0.045191419

0.046723744

0.064333317

0.075886559

0.077297271

0.078707983

0.100111884

0.108673445

Table 3.1

letter

frequency

letter

frequency

letter

frequency

letter

frequency

707

2708

8

372

495

64

0

391

86

155

419

555

56

70

23

191

457

0

672

2

16

295

133

1581

195

79

550

2153

23

599

1020

62

20

23

52

4

322

0

527

9

16

21

501

0

13

963

Total

16,799

2

31

158

Here if N2 represents the total word tokens in the text (where words formed by numerals 1, 2 etc. have been excluded), then N2 = 16,799.

A table similar to the table 2.2 can be constructed for the rank frequency profile of words initials for which the Zipfs order can be demonstrated with the help of following figure-

_1296361989.xls

Chart1

00.000119

00.000119

00.000238

00.000476

00.000536

00.000774

00.000952

00.000952

00.001191

00.00125

00.001369

00.001369

00.001369

00.001845

00.003096

00.003334

00.003691

00.00381

00.004167

00.004643

00.00512

00.007918

00.009227

00.009406

00.01137

00.011609

00.017562

00.019169

00.022145

00.023277

00.024943

00.027206

00.028932

00.029825

00.031373

00.032742

00.03304

00.035659

00.040005

00.042624

00.057328

00.060722

00.094118

00.12817

00.16121

Zipf order(i)

normalized frequencies

Zipf's order(i) of word's initials

normalized frequencies

Sheet1

0.000119

0.000119

=0.000238

0.000476

K0.000536

0.000774

0.000952

0.000952

0.001191

0.00125

0.001369

0.001369

0.001369

0.001845

0.003096

0.003334

{k0.003691

0.00381

0.004167

0.004643

0.00512

0.007918

0.009227

0.009406

0.01137

0.011609

0.017562

0.019169

0.022145

0.023277

0.024943

0.027206

0.028932

0.029825

0.031373

0.032742

0.03304

0.035659

0.040005

0.042624

0.057328

0.060722

0.094118

0.12817

0.16121

4. Mathematical models for frequencies of letters

After obtaining the rank frequency profile of texts for different letters and for different words initials we have tried to formulate these in the form of mathematical equations. For this we have tested following models available in literature for rank frequency distributions:

Distributions specified for rank frequency distribution of word frequencies, Zipfs distribution and Zipf Mandelbrot distribution as given in the book by Manning and Schutze (1999); various rank frequency distributions used for linguistic components as- Good, Geometric series distribution, Borodovsky and Gusein Zade equation as cited in the research paper of Y. Tambovtsev and C. Martindale (2007) and Yule equation as concluded for the phoneme frequencies by the authors; negative hypergeometric distribution and determination of frequencies by Zipfs order.

1. Zipf Distribution: Zipf's law has been defined in the work of Manning and Schutze (1999) as a relation between the frequency of occurrence of an event and its rank when the events are ranked with respect to the frequency of occurrence (the most frequent one first). According to Zipfs law if the frequency of occurrence of an event ranked in descending order of frequency, then

c being a constant, where

is the frequency of event of rth rank. General form of this formula was given by him in the later works as

..(4.1) , where

and b are parameters of text.

2. Zipf Mandelbrot: The modification to Zipf formula has been introduced by Mandelbrot as cited in the book of Manning and Schutze (1999) by including an additional parameter c to express the formula of rank frequency distribution in the form

.(4.2), where

, b and c are parameters.

3. Good distribution: Good has suggested an equation for ranked distribution of phoneme and grapheme frequencies as-

.(4.3), where n is number of symbols and

is normalized frequency of event of rank r.

_1294717890.unknown

_1295977773.unknown

_1296015878.unknown

_1296015879.unknown

_1296015499.unknown

_1295956600.unknown

_1294589519.unknown

4. Geometric series distribution: Sigurd has suggested a geometric-series equation for the ranked distribution of phoneme frequencies in the form:

, where

is the frequency of the most frequent phoneme, k is the parameter to be estimated, and r is rank. To reduce the dependency of this equation on most frequent phoneme he has modified the equation as

, where n is the number of symbols, and k is the parameter to be estimated and

be the normalized frequency corresponding to rank r.

Thus the general form of the geometric series equation is:

..(4.4) where

and b are parameters and

be the frequency for rank r.

5. Equation given by Borodovsky and Gusein Zade: Gusein-Zade and Borodovsky have suggested a parameter-free equation, by assuming that

rather than, as assumed in Zipfs equation that

depends on

as-

(4.5), where n is the number of symbols, and have presented evidence from distributions of letter frequencies of four languages.

The references of the works cited at serial numbers 3, 4 and 5 are available in the research paper of Y. Tambovtsev and C. Martindale (2007).

6. Yule distribution: Y. Tambovtsev and C. Martindale (2007) proposed Yule equation, and have showed that the Yule equation fits the distribution of phoneme frequencies better than the Zipf equation or equation proposed by Sigurd and Borodovsky and Gusein-Zade. Its value has been given as-

(4.6),where a, b, c are parameters.

7. Negative hypergeometric: P. Grzybek, and E. Kelih (2005) explored that grapheme frequencies of Slovean alphabets in text follow negative hypergeometric distribution. P. Grzybek (2007) examined the regularity of parameters of negative hypergeometric distribution for German letter frequencies and has concluded that parameter behaviour follow clear rules as well. The negative hypergeometric distribution has been characterized by them in the form of the recurrence relation:

_1294574240.unknown

_1294718170.unknown

_1296015681.unknown

_1296015880.unknown

_1296015881.unknown

_1295021290.unknown

_1294718120.unknown

_1294718139.unknown

_1294589594.unknown

_1293992341.unknown

_1293992365.unknown

_1293986727.unknown

and the distribution has been given as:

..(4.7), with r =1, 2, ...... n+1; where

>b>0 are parameters and n({1,2,3..}is the inventory size and

is the normalized frequency corresponding to the rank r.

Besides these distributions, we have tested the applicability of the following equation, proposed by Ali Eftekhari (2006), for expressing the relation between Zipfs order of letters of English texts and their frequencies

..(4.8), where

and b are parameters and i is the Zipf order of letter of rank r.

Application of the distributions discussed above in the form of equations (4.1) to (4.8) to the frequencies of different letters, ranks of letters and their Zipf orders for the text Tanav se Mukti has enabled us to calculate the theoretical values of the frequencies and the values of determination coefficient(

) for each model, defined in the following manner-

If a data set has n observed values yi i = 1,2, ..n each of which has an associated modelled value fi and if

be the mean of the observed data then the coefficient of determination is obtained by the formula-

..(4.9), where

is the total sum of squares, and

is the sum of squared error or the residual sum of squares.

R2 is a statistic that gives information about the goodness of fit of a model.The calculated values of determination coefficient for rank frequency distribution of letters for their occurrences in the text and in the starting position of the words in the text Tanav se Mukti have been shown in the Table 4.1. We have used the software Datafit for determination of parameters for all the equations except (4.2). This software was producing numerical errors for equation (4.2) and as such we were left with no option but to apply the least square method for linear relation

by first setting c = 0 and then increasing it by small steps until the goodness of fit stops improving.

_1294820669.unknown

_1295011274.unknown

_1296015730.unknown

_1296015814.unknown

_1296015853.unknown

_1295021634.unknown

_1295010951.unknown

_1295010968.unknown

_1294820752.unknown

_1294820393.unknown

_1294820658.unknown

_1294669400.unknown

Table 4.1. Distributions, parameters and determination coefficients for the text Tanav se Mukti

Distribution

For occurrence of letters in the text

For occurrence of letters in the words initials

Determination coefficient

Parameters

Determination coefficient

Parameters

Zipf

0.836

b = 0.685

0.932

b = 0.815

Zipf Mandelbrot

0.985

0.925

EMBED Equation.3

EMBED Equation.3

Good

0.900

&

0.825

&

Geometric series

0.9891

b = 0.889

0.937

b = 0.843

Borodovsky & Gusein-Zade equation

0.866

&

0.772

&

Yule

0.9894

b = 0.0382, c = 0.8958

0.981

b = 0.459, c = 0.936

Negative hypergeometric

0.939

b = 0.6872

0.976

b = 0.337

, i be Zipf order of letter of rank r

0.978

EMBED Equation.3

0.892

b = -4.673

Thus the highest determination coefficient in both cases has been obtained for the Yule distribution (0.9894 and 0.981 respectively) and corresponding theoretical and empirical frequencies for the text Tanav se Mukti for different ranks have been shown in the following figures-

_1295238680.unknown

_1295348772.unknown

_1295926793.unknown

_1295927310.unknown

_1295927360.unknown

_1295927396.unknown

_1295927252.unknown

_1295348805.unknown

_1295348616.unknown

_1295348685.unknown

_1295241857.unknown

_1295006756.unknown

_1295006786.unknown

_1295006793.unknown

_1295006771.unknown

_1295006612.unknown

_1295006722.unknown

_1295000463.unknown

The first figure shows the empirical and calculated values of the frequencies of letters in the text while the second figure represents the same for the beginning letter of words in the text.

EMBED Excel.Chart.8 \s


_1295007972.xls

Chart3

44684543.5905287838

41163963.569357242

32363495.8031044049

31783097.1463167844

31202750.7258343585

26452446.8661260312

19212178.9161742352

18581941.8378059247

18501731.5964174633

15531544.8507202785

12601378.7740980683

11281230.9414788749

8481099.2521425765

805981.8738743296

716877.2006766502

711783.8195982592

679700.48399669

661626.0915304196

589559.6657485043

543500.3404952371

517447.3465694217

490400.0002241208

458357.6931922757

449319.8839934186

361286.0903270481

341255.8823954834

322228.8770271975

316204.7324934107

294183.1439278683

270163.8392734482

194146.5756903786

167131.1363700072

143117.3277056717

128104.9767786169

12593.9291223011

12284.046733052

11775.2062989733

9967.2976224148

9260.2222142626

8453.8920408715

5448.2284066932

2543.1609576111

2338.6267917046

1734.5696656731

1630.9392864739

327.6906789001

224.7836208551

observed

theoretical

Rank

Frequency

Data Table

144684543.5905287838-75.5905287838-1.691820250375.5905287838-259.8031044049369.2741656415

241163963.569357242152.4306427583.7033683858152.430642758

332363495.8031044049-259.8031044049-8.0285260941259.8031044049

431783097.146316784480.85368321562.544168760780.8536832156

531202750.7258343585369.274165641511.8357104372369.2741656415

626452446.8661260312198.13387396887.4908837039198.1338739688

719212178.9161742352-257.9161742352-13.4261412928257.9161742352

818581941.8378059247-83.8378059247-4.51226081483.8378059247

918501731.5964174633118.40358253676.4001936506118.4035825367

1015531544.85072027858.14927972150.52474434788.1492797215

1112601378.7740980683-118.7740980683-9.4265157197118.7740980683

1211281230.9414788749-102.9414788749-9.1260176308102.9414788749

138481099.2521425765-251.2521425765-29.6287903982251.2521425765

14805981.8738743296-176.8738743296-21.9719098546176.8738743296

15716877.2006766502-161.2006766502-22.5140609847161.2006766502

16711783.8195982592-72.8195982592-10.241856295272.8195982592

17679700.48399669-21.48399669-3.164064313721.48399669

18661626.091530419634.90846958045.281160299634.9084695804

19589559.665748504329.33425149574.980348301529.3342514957

20543500.340495237142.65950476297.856262387342.6595047629

21517447.346569421769.653430578313.472617133169.6534305783

22490400.000224120889.999775879218.367301199889.9997758792

23458357.6931922757100.306807724321.9010497215100.3068077243

24449319.8839934186129.116006581428.7563489045129.1160065814

25361286.090327048174.909672951920.750601925774.9096729519

26341255.882395483485.117604516624.961174345185.1176045166

27322228.877027197593.122972802528.92017788993.1229728025

28316204.7324934107111.267506589335.2112362625111.2675065893

29294183.1439278683110.856072131737.7061469836110.8560721317

30270163.8392734482106.160726551839.3187876118106.1607265518

31194146.575690378647.424309621424.445520423447.4243096214

32167131.136370007235.863629992821.475227540635.8636299928

33143117.327705671725.672294328317.952653376425.6722943283

34128104.976778616923.023221383117.986891705623.0232213831

3512593.929122301131.070877698924.856702159131.0708776989

3612284.04673305237.95326694831.109235203337.953266948

3711775.206298973341.793701026735.721111988641.7937010267

389967.297622414831.702377585232.022603621431.7023775852

399260.222214262631.777785737434.541071453731.7777857374

408453.892040871530.107959128535.842808486330.1079591285

415448.22840669325.771593306810.68813575345.7715933068

422543.1609576111-18.1609576111-72.643830444318.1609576111

432338.6267917046-15.6267917046-67.942572628815.6267917046

441734.5696656731-17.5696656731-103.350974547817.5696656731

451630.9392864739-14.9392864739-93.37054046214.9392864739

46327.6906789001-24.6906789001-823.02263000424.6906789001

47224.7836208551-22.7836208551-1139.181042756622.7836208551

&CData Table

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00

00

observed

theoretical

Rank

Frequency

27082791.7791102572

21531902.1588720045

15811478.6208494178

10201213.1203147003

9631025.1634110695

716882.6840278384

672769.8799504093

599677.8657200599

555601.170989768

550536.1968376391

527480.4523740619

501432.1432891694

486389.9346785229

457352.8067364728

419319.9629583912

391290.7695240033

372264.7139771662

322241.3762760525

295220.4080194537

195201.5172232135

191184.4569540059

158169.0167007263

155155.0157256037

133142.2978713636

86130.7274558177

78120.1859899754

70110.5695278144

64101.7865062419

6293.7559695751

5686.4060986606

5279.6729835747

3173.4995927521

2367.8349017806

2362.6331529409

2357.853222549

2153.4580777615

2049.4143080685

1645.6917194973

1642.262981745

1339.1033202108

936.190246292

833.5033204338

431.0239433324

228.7351714289

226.6215534436

observed

theoretical

Rank

Frequency

_1295198153.xls

Chart4

27082791.7791102572

21531902.1588720045

15811478.6208494178

10201213.1203147003

9631025.1634110695

716882.6840278384

672769.8799504093

599677.8657200599

555601.170989768

550536.1968376391

527480.4523740619

501432.1432891694

486389.9346785229

457352.8067364728

419319.9629583912

391290.7695240033

372264.7139771662

322241.3762760525

295220.4080194537

195201.5172232135

191184.4569540059

158169.0167007263

155155.0157256037

133142.2978713636

86130.7274558177

78120.1859899754

70110.5695278144

64101.7865062419

6293.7559695751

5686.4060986606

5279.6729835747

3173.4995927521

2367.8349017806

2362.6331529409

2357.853222549

2153.4580777615

2049.4143080685

1645.6917194973

1642.262981745

1339.1033202108

936.190246292

833.5033204338

431.0239433324

228.7351714289

226.6215534436

observed

theoretical

Rank

Frequency

Data Table

144684543.5905287838-75.5905287838-1.691820250375.5905287838-259.8031044049369.2741656415

241163963.569357242152.4306427583.7033683858152.430642758

332363495.8031044049-259.8031044049-8.0285260941259.8031044049

431783097.146316784480.85368321562.544168760780.8536832156

531202750.7258343585369.274165641511.8357104372369.2741656415

626452446.8661260312198.13387396887.4908837039198.1338739688

719212178.9161742352-257.9161742352-13.4261412928257.9161742352

818581941.8378059247-83.8378059247-4.51226081483.8378059247

918501731.5964174633118.40358253676.4001936506118.4035825367

1015531544.85072027858.14927972150.52474434788.1492797215

1112601378.7740980683-118.7740980683-9.4265157197118.7740980683

1211281230.9414788749-102.9414788749-9.1260176308102.9414788749

138481099.2521425765-251.2521425765-29.6287903982251.2521425765

14805981.8738743296-176.8738743296-21.9719098546176.8738743296

15716877.2006766502-161.2006766502-22.5140609847161.2006766502

16711783.8195982592-72.8195982592-10.241856295272.8195982592

17679700.48399669-21.48399669-3.164064313721.48399669

18661626.091530419634.90846958045.281160299634.9084695804

19589559.665748504329.33425149574.980348301529.3342514957

20543500.340495237142.65950476297.856262387342.6595047629

21517447.346569421769.653430578313.472617133169.6534305783

22490400.000224120889.999775879218.367301199889.9997758792

23458357.6931922757100.306807724321.9010497215100.3068077243

24449319.8839934186129.116006581428.7563489045129.1160065814

25361286.090327048174.909672951920.750601925774.9096729519

26341255.882395483485.117604516624.961174345185.1176045166

27322228.877027197593.122972802528.92017788993.1229728025

28316204.7324934107111.267506589335.2112362625111.2675065893

29294183.1439278683110.856072131737.7061469836110.8560721317

30270163.8392734482106.160726551839.3187876118106.1607265518

31194146.575690378647.424309621424.445520423447.4243096214

32167131.136370007235.863629992821.475227540635.8636299928

33143117.327705671725.672294328317.952653376425.6722943283

34128104.976778616923.023221383117.986891705623.0232213831

3512593.929122301131.070877698924.856702159131.0708776989

3612284.04673305237.95326694831.109235203337.953266948

3711775.206298973341.793701026735.721111988641.7937010267

389967.297622414831.702377585232.022603621431.7023775852

399260.222214262631.777785737434.541071453731.7777857374

408453.892040871530.107959128535.842808486330.1079591285

415448.22840669325.771593306810.68813575345.7715933068

422543.1609576111-18.1609576111-72.643830444318.1609576111

432338.6267917046-15.6267917046-67.942572628815.6267917046

441734.5696656731-17.5696656731-103.350974547817.5696656731

451630.9392864739-14.9392864739-93.37054046214.9392864739

46327.6906789001-24.6906789001-823.02263000424.6906789001

47224.7836208551-22.7836208551-1139.181042756622.7836208551

&CData Table

Page &P

Data Table

00

00

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00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

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00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

observed

theoretical

Rank

Frequency

27082791.7791102572

21531902.1588720045

15811478.6208494178

10201213.1203147003

9631025.1634110695

716882.6840278384

672769.8799504093

599677.8657200599

555601.170989768

550536.1968376391

527480.4523740619

501432.1432891694

486389.9346785229

457352.8067364728

419319.9629583912

391290.7695240033

372264.7139771662

322241.3762760525

295220.4080194537

195201.5172232135

191184.4569540059

158169.0167007263

155155.0157256037

133142.2978713636

86130.7274558177

78120.1859899754

70110.5695278144

64101.7865062419

6293.7559695751

5686.4060986606

5279.6729835747

3173.4995927521

2367.8349017806

2362.6331529409

2357.853222549

2153.4580777615

2049.4143080685

1645.6917194973

1642.262981745

1339.1033202108

936.190246292

833.5033204338

431.0239433324

228.7351714289

226.6215534436

observed

theoretical

Rank

Frequency

5. Validation of models for different texts

We have counted the frequency of letters for texts obtained from different sources in the following forms-

1. Text composed of 5 stories.(say, Text 1)

2. Text containing 29 short stories.(Text 2)

3. Text containing 62 articles.(Text 3)

4. Text containing 37 articles.(Text 4)

5. Poetic text containing 180 poems (text 5), and

6. Text formed as mixture of all the considered texts, from text 1 to text 5 above and the text Tanav se Mukti.(Text 6)

The calculated values of the determination coefficients greater than 0.98 for letter frequencies in the texts and greater than 0.95 for the letter frequencies in the words initials and the Zipfs orders for the occurrence of letters in text and for occurrence as words initials have been given in the following tables:

Table 5.1(a). Calculated values of determination coefficients (which are >0.98) for different texts for rank frequency distribution of letters.

Text

Total counted letters(N1)

Determination coefficient & distribution



Text1

18,162

0.990(Yule)

0.989(Geometric series)

0.981(Zipf Mandelbrot)

Text 2

22,375

0.996(Yule)



Text 3

70,622

0.992(Yule)

0.981(Negative hypergeometric)


Text 4

82,803

0.992(Yule)



Text 5

90,908

0.991(Yule)


&

Text 6

3,25,983

0.992(Yule)



Sources of the texts have been given in the Appendix.

Table 5.1(b).

Text

Zipfs order of letters for their instances in text

Text 1

Text 2

Text 3

Text 4

Text 5

Text 6

Table 5.2(a). Calculated values of determination coefficients (which are >0.95) for different texts for rank frequency distribution of words initials.

Text

Total counted words(N2)




Text 1

8,298

0.978(Yule)


&

Text 2

9,831

0.960(Yule)


&

Text 3

29,623

0.975(Yule)


0.962(Zipf)

Text 4

34,404

0.984(Yule)

0.979( Negative hypergeometric)

0.963(Zipf)

Text 5

40,418

0.987(Yule)



Text 6

1,39,373

0.985(Yule)


&

Table 5.2(b).

Text

Zipfs order of letters for their instances in the beginning of words in the texts

Text 1

Text 2

Text 3

Text 4

Text 5

Text 6

The variations in the values of the parameters of the models for different considered texts have been depicted in the following figures, where the first figure represents the parameters of the model for letter frequencies and the second one for the letter frequencies in the words initials. As the value of parameter

increases with the size of text, for comparison we have drawn the values of

and

, where N1 denotes total counted letters in the text and N2 total counted word tokens in the texts.

Parameters of the Yule distribution for different texts for rank frequency distribution of letters and for distribution of the word initials.

From the figure although the parameters of the model for the distributions of letters in the text and in the starting position of words of the texts lies in slight different ranges but their manner of change for the two is almost the same.



_1295352040.xls

Chart4

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0.15233404540.5010.959

0.17814097150.6580.971

0.18097602020.6210.962

0.14095325360.2760.927

0.16233075860.4980.952

0.17752821760.4590.936

a/N2

b

c

sampadakiy

full000000

2426383713481812203513161041

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0.18830658770.08359369170.22557020750.08416105880.2614002370.32443599210.2623264371

0.02083319130.07147680030.17335157020.02807489790.10479013880.11101418390.0389805996

0.0368810910.01282632760.05012859330.00497616480.03944764890.03541353030.0488219535

0.0055182496000000

0.3654493220.27263445650.18792109790.41146851350.43211846170.35768108840.4930830755

0.05743696220.00387892610.46277529580.01280197940.01354683720.01147984040.2490739961

0.32569462750.15788940890.33988246370.11588981820.13619351730.21582928040.073600381

0.07576483010.00498586950.00774130830.00497616480.04903352080.0021133130.0553534586

0.22710452860.23926856320.03201467180.30412095650.33460652860.16779443760.2119989992

0.02702698610.07204366870.05761847690.02292059560.16913757110.03216630110.0768862554

0000000

0000.004976164800.01553217260

2.85895016812.08079698572.92794512432.41654029752.8608884872.86996946152.6472023827

2765543117533060194318692357

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515255129370142408327

96651090356245677176

32412035891374569408

19982432310111631

3812473292741

94564027310119366781442

6631330987376

76728369913914429669

9445338148

42852127576565205294

269956181952473

00030100

7937892467116708557859316051

0.34836840120.60858359480.2612129340.45617173520.34833273570.31512392510.389522393

0.12397631350.106230390.13232007150.12522361360.11599139480.16017534990.0841183275

0.06488597710.02857463020.01922217260.05515802030.02545715310.06879109760.0540406544

0.12170845410.05714926040.13455520790.08378056050.08174973110.12999494180.0125599075

0.04082146910.01344688480.05334525410.01356589150.06704912150.09593660430.0674268716

0.00239385160.01098162260.03620920880.00342874180.01810684830.01955825320.0051231201

0.00478770320.00134468850.00700342720.00044722720.00519899610.0045523520.0067757395

0.11906261810.0717167190.04067948140.15071556350.16780207960.11431461810.2383077177

0.00831548440.00033617210.19818208910.00134168160.00143420580.00118023940.0621384895

0.09663600860.03171223670.10415735360.02072152650.02581570460.04990726690.0114030739

0.01184326570.00044822950.00074504540.00044722720.00681247760.00016860560.0079325731

0.05392465670.05838189150.00402324540.08586762080.10129078520.03456415440.0485870104

0.00327579690.011093680.0083445090.00268336310.03495876660.00404653520.0120641216

0000.000447227200.00168605630

0.52997783910.43603350110.50589154930.5165465370.52997503240.52499923320.5298368607

0.37339974390.34362679390.38609623060.37534794620.36049085250.42322747520.3004232252

0.25603678670.14656274620.10958723550.23057627310.13481561210.26564606310.2275009439

0.36981098090.2359762320.38936642340.29970322710.29533252880.38263655030.0793161968

0.18837181560.08359369170.22557020750.08416105880.2614002370.32443599210.2623264371

0.02084195050.07147680030.17335157020.02807489790.10479013880.11101418390.0389805996

0.03689619780.01282632760.05012859330.00497616480.03944764890.03541353030.0488219535

0.36554695160.27263445650.18792109790.41146851350.43211846170.35768108840.4930830755

0.05745986420.00387892610.46277529580.01280197940.01354683720.01147984040.2490739961

0.32578852370.15788940890.33988246370.11588981820.13619351730.21582928040.073600381

0.07579440450.00498586950.00774130830.00497616480.04903352080.0021133130.0553534586

0.22717978490.23926856320.03201467180.30412095650.33460652860.16779443760.2119989992

0.02703822570.07204366870.05761847690.02292059560.16913757110.03216630110.0768862554

0000.004976164800.01553217260

2.85414306892.08079698572.92794512432.41654029752.8608884872.86996946152.6472023827

cheele

full1100

5961116433457458228329

256144165130123165126

126101866422659

17889214697212317

62261261388162117

8163011617

30110010

0000000

25313322298292118229

100174034116

1312717332187228

11000800

0000030

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1000000

0001020

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after half

24740143416

8125143146

02010170

6235230

1200072

0000000

1000000

0000000

06373051

0000000

0260020

0100000

0000000

0000000

0000000

0000000

4097

k+half

89792888337106

0300000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

01041300

0000000

0000000

0000000

4

6201193433471461269335

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126121867424359

18491217747412617

63281261388169119

8163011617

40110010

0000000

25313959301292123230

100174034116

1312917932187428

11100800

89802929640106

61811419015

1000000

0001020

1770176314761190124310311164

s_t_r0

s_t_ree0

s_t_ro0

0.35028248590.67668746450.29336043360.39579831930.37087691070.26091173620.2878006873

0.14915254240.0884855360.14634146340.1126050420.10136765890.17361784680.1134020619

0.07118644070.00680657970.0121951220.0563025210.03378921960.04170708050.0506872852

0.10395480230.05161656270.14701897020.06218487390.0595333870.12221144520.014604811

0.03559322030.01588201930.08536585370.01092436970.07079646020.16391852570.102233677

0.0045197740.00907543960.02032520330.00084033610.01287208370.00096993210.0060137457

0.00225988700.0074525745000.00096993210

0000000

0.14293785310.07884288150.03997289970.25294117650.2349155270.11930164890.1975945017

0.005649717500.117886178900.00241351570.00387972840.0996563574

0.07401129940.01644923430.12127371270.02689075630.01448109410.07177497580.0240549828

0.00621468930.000567215000.006436041800

0.05028248590.0453771980.00135501360.07731092440.0772325020.03879728420.0910652921

0.00338983050.01020986950.00745257450.00336134450.015285599400.0128865979

0.0005649718000000

0000.000840336100.00193986420

0.53012075060.38127172370.51902905940.52924671310.53072027540.50574250490.5171369839

0.40944453940.30955908580.40574480540.35477982650.33474952760.43856091020.356137046

0.27138077340.04899957520.0775311220.23369243420.16513782190.1911670670.2180684754

0.33951344110.22071356370.40664355890.24919297850.24231024450.37061215850.0890515572

0.1712836070.09491828220.30306560460.07118653770.27045514780.42765510340.3363546838

0.03520693170.06156611920.11423956120.00858550070.08083167280.00970885410.0443665317

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0000000

0.40116081230.28894935930.1856674820.50161426940.49092318460.36593563120.4622496711

0.042189861900.363623869100.02098466950.03107595970.3315461721

0.27799462950.09747546070.36911609750.14028224160.0884749320.27277184150.1293561613

0.04555430640.0061167423000.046851878200

0.21690859830.20246800520.01290986040.28552346130.28534691530.18187780880.3148086067

0.02781210560.0675269720.0526751350.02761931380.092197890800.0809018653

0.0060957817000000

0000.008585500700.01747784410

2.79452949191.77956488942.86292129062.41030877762.64898416052.82229453762.8799777545

6201193433471461269335

265156216134126179132

126121867424359

18491217747412617

63281261388169119

8163011617

40110010

25313959301292123230

100174034116

1312917932187428

11100800

89802929640106

61811419015

0001020

1770176314761190124310311164

0.35028248590.67668746450.29336043360.39579831930.37087691070.26091173620.2878006873

0.14971751410.0884855360.14634146340.1126050420.10136765890.17361784680.1134020619

0.07118644070.00680657970.0121951220.0563025210.03378921960.04170708050.0506872852

0.10395480230.05161656270.14701897020.06218487390.0595333870.12221144520.014604811

0.03559322030.01588201930.08536585370.01092436970.07079646020.16391852570.102233677

0.0045197740.00907543960.02032520330.00084033610.01287208370.00096993210.0060137457

0.00225988700.0074525745000.00096993210

0.14293785310.07884288150.03997289970.25294117650.2349155270.11930164890.1975945017

0.005649717500.117886178900.00241351570.00387972840.0996563574

0.07401129940.01644923430.12127371270.02689075630.01448109410.07177497580.0240549828

0.00621468930.000567215000.006436041800

0.05028248590.0453771980.00135501360.07731092440.0772325020.03879728420.0910652921

0.00338983050.01020986950.00745257450.00336134450.015285599400.0128865979

0000.000840336100.00193986420

0.53012075060.38127172370.51902905940.52924671310.53072027540.50574250490.5171369839

0.4101788420.30955908580.40574480540.35477982650.33474952760.43856091020.356137046

0.27138077340.04899957520.0775311220.23369243420.16513782190.1911670670.2180684754

0.33951344110.22071356370.40664355890.24919297850.24231024450.37061215850.0890515572

0.1712836070.09491828220.30306560460.07118653770.27045514780.42765510340.3363546838

0.03520693170.06156611920.11423956120.00858550070.08083167280.00970885410.0443665317

0.019863352900.052675135000.00970885410

0.40116081230.28894935930.1856674820.50161426940.49092318460.36593563120.4622496711

0.042189861900.363623869100.02098466950.03107595970.3315461721

0.27799462950.09747546070.36911609750.14028224160.0884749320.27277184150.1293561613

0.04555430640.0061167423000.046851878200

0.21690859830.20246800520.01290986040.28552346130.28534691530.18187780880.3148086067

0.02781210560.0675269720.0526751350.02761931380.092197890800.0809018653

0000.008585500700.01747784410

2.78916801271.77956488942.86292129062.41030877762.64898416052.82229453762.8799777545

TANAV SE MUKTI

full123

1673222157712101046607674

681204223643203660335

2341221591605919893

3269541210012415117

7988941271418849

81313412627

4101403215

0000000

53417742512416321442

73111233613

493171464431313114

1903101513

300190127

31843151614

1000001

72090161

243689325409371598

after half

153260687214110

288107224926

9110102056

07060125

32000230

0300020

3200003

0000000

1643842172

0000000

04710065

0000000

0000000

0100010

0000000

0000050

5939

k+half

299432729441236656

0200061

0000000

0003000

0000000

0000000

0000000

0000000

0000000

0000000

0010010

0100000

0000000

0220101372

0000000

0000000

0000000

25

1688255057712781053827785

709285223650225709361

2431331591645940499

32610241410612416322

82909412714111149

81613412827

4421403218

0000000

53524180516418338444

73111333713

493219465431313719

1903101513

303454732342538565

319163154714

1000001

72090211

4468411631783236264531201921

s_t_r1

s_t_ree0

s_t_ro0

EXTRA1(k_)hee2ti1

0.37779767230.61953352770.181560730.39493201480.39810964080.26506410260.4086413326

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0.07296329450.02478134110.13027061040.03275648950.04688090740.05224358970.0114523686

0.01835273050.02186588920.02957835120.03924598270.05330812850.03557692310.0255075482

0.00179051030.00388726920.0040906230.00123609390.0045368620.00256410260.0140551796

0.00984780660.00048590860.004405286300.00113421550.00064102560.0093701197

0000000

0.1197403760.05855199220.02517306480.15945611870.15803402650.10833333330.23112962

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0.1103401970.05320699710.14631843930.01328800990.00491493380.04391025640.0098906819

0.00425246200.00094398990.00309023490.00567107750.00032051280.0015616866

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0.00067144140.00461613220.0050346130.00092707050.05822306240.00224358970.0072878709

0.0002238138000000.0005205622

0.00156669650.000485908600.002781211400.00673076920.0005205622

0.53054666690.4279401420.44690736150.52933676760.52899307640.50775329460.5275939477

0.42142840250.26673459910.26896154270.46514369280.30243324520.48577600770.4532301022

0.22845703560.16000536020.21618698940.2180472180.1223811450.38187307940.2204842442

0.27555940310.132198590.38304984620.16155747730.2069724410.22248466410.0738472796

0.10585600720.12059418740.15023774970.18333019870.22546676460.17122868710.1350097168

0.01633914680.03112547040.03245280930.01194066240.03531533990.02207007770.0864780667

0.06564530020.00534840980.034478187200.0110972660.00679957070.0631332131

0000000

0.36664723330.23971993230.13371869890.42236236610.42063804220.34736551170.4884291078

0.01459856980.00759625710.53011634270.00934026580.0110972660.01974353450.0487733613

0.35087847570.22518479240.40571418320.0828338810.0376907220.19800444150.0658691158

0.033498709300.0094860990.02576658780.04231849570.00372029820.0145591035

0.26327631260.35081082750.01944173680.33184412510.42383233070.37248943460.1653007857

0.00707729470.035817030.03843374910.00934026580.23884645820.01974353450.0517459742

0.0027138347000000.0056781061

0.01459856980.005348409800.023612681700.04856258680.0056781061

2.69712096222.00842400792.66918529542.47445619012.60708259292.80761472322.405810231

1688255057712781053827785

710285223650225709362

2431331591645940499

32610241410612416322

82909412714111149

81613412827

4421403218

53524180516418338444

73111333713

493219465431313719

1903101513

303454732342538565

319163154714

72090211

4468411631783236264531201921

0.37779767230.61953352770.181560730.39493201480.39810964080.26506410260.4086413326

0.15890778870.06924198250.07016991820.20086526580.08506616260.22724358970.188443519

0.05438675020.03231292520.05003146630.05067985170.02230623820.12948717950.0515356585

0.07296329450.02478134110.13027061040.03275648950.04688090740.05224358970.0114523686

0.01835273050.02186588920.02957835120.03924598270.05330812850.03557692310.0255075482

0.00179051030.00388726920.0040906230.00123609390.0045368620.00256410260.0140551796

0.00984780660.00048590860.004405286300.00113421550.00064102560.0093701197

0.1197403760.05855199220.02517306480.15945611870.15803402650.10833333330.23112962

0.00156669650.0007288630.35022026430.00092707050.00113421550.00224358970.0067673087

0.1103401970.05320699710.14631843930.01328800990.00491493380.04391025640.0098906819

0.00425246200.00094398990.00309023490.00567107750.00032051280.0015616866

0.06781557740.11030126340.00220264320.09981458590.16068052930.12339743590.0338365435

0.00067144140.00461613220.0050346130.00092707050.05822306240.00224358970.0072878709

0.00156669650.000485908600.002781211400.00673076920.0005205622

0.53054666690.4279401420.44690736150.52933676760.52899307640.50775329460.5275939477

0.42169967810.26673459910.26896154270.46514369280.30243324520.48577600770.4537335356

0.22845703560.16000536020.21618698940.2180472180.1223811450.38187307940.2204842442

0.27555940310.132198590.38304984620.16155747730.2069724410.22248466410.0738472796

0.10585600720.12059418740.15023774970.18333019870.22546676460.17122868710.1350097168

0.01633914680.03112547040.03245280930.01194066240.03531533990.02207007770.0864780667

0.06564530020.00534840980.034478187200.0110972660.00679957070.0631332131

0.36664723330.23971993230.13371869890.42236236610.42063804220.34736551170.4884291078

0.01459856980.00759625710.53011634270.00934026580.0110972660.01974353450.0487733613

0.35087847570.22518479240.40571418320.0828338810.0376907220.19800444150.0658691158

0.033498709300.0094860990.02576658780.04231849570.00372029820.0145591035

0.26327631260.35081082750.01944173680.33184412510.42383233070.37248943460.1653007857

0.00707729470.035817030.03843374910.00934026580.23884645820.01974353450.0517459742

0.01459856980.005348409800.023612681700.04856258680.0056781061

2.69467840312.00842400792.66918529542.47445619012.60708259292.80761472322.4006355583

katha

full

9041124462650607348318

349314236202163218109

230324067285648

2388522485704123

523012912576790

4274884015

8030208

0000000

35712138525310117283

211262011273

21561112401911511

7103903

0004000

7815374327

0120000

0001010

14886811109747

after half

6132015154045

202415781513

32030442

0823125

2500150

0000000

1000000

0000000

011342052

0000000

020331040

0000000

0000000

0000000

0000000

0000000

84

k+half

1131580921279557

01000713

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

09011170

0000000

0000000

0000000

10

9101268462665622395376

369338251209171233122

2333440702810050

2389422688714328

543512912587290

4274884015

9030208

0000000

35713272527310122285

211262011273

21581145411911911

7103903

11316709713810257

7815374327

0120000

0001010

2537218716551724151711921145

s_t_r11

s_t_ree1

s_t_ro0

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0.09184075680.01554641060.02416918430.04060324830.01845748190.08389261740.0436681223

0.09381158850.04298125290.13655589120.05104408350.04680290050.03607382550.0244541485

0.02128498230.0160036580.07794561930.00696055680.03823335530.06040268460.0786026201

0.00157666540.0123456790.02900302110.00464037120.002636783100.0131004367

0.00354749700.001812688800.001318391600.0069868996

0000000

0.14071738270.06035665290.04350453170.30568445480.20435069220.10234899330.2489082969

0.00827749310.00045724740.158308157100.00725115360.00167785230.0637554585

0.08474576270.0370370370.08761329310.02378190260.01252471980.09983221480.0096069869

0.00275916440.000457247400.00174013920.00593276200.0026200873

0.04454079620.076360310900.05626450120.09096901780.08557046980.0497816594

0.00275916440.0036579790.00906344410.00174013920.04878048780.00251677850.023580786

00.00045724740.00120845920000

0000.000580046400.00083892620

0.53057091560.45594570930.51388538050.53012285180.52738162250.52803403740.5275634758

0.40455181890.41633471750.41268221080.36904562050.35498031530.46032793080.3441992441

0.31636584420.09339155860.12980513370.18767881260.10630864370.29994230960.1972609473

0.320281210.19514127730.39224813160.21908694590.20674049820.17289837410.1309220567

0.11821722360.09546909330.28694808690.04988339830.18004180210.2445851790.2884149265

0.01467703240.07826975310.1481373680.0359700420.022589335200.081933292

0.028873017400.016509340800.012613059200.0500341092

0000000

0.39810742290.24446517010.19675753230.52268523560.46814311080.33656762110.4993881446

0.05725202920.00507303960.420971864100.05153810890.01546840360.2531925194

0.30175550460.17610694450.30775977620.12827939340.07914467980.33187729870.0643831466

0.02345718180.005073039600.0159511280.043885117500.0224703128

0.19993155660.2833756500.23358945940.31461461180.303496480.2154670625

0.02345718180.02961037950.06150203840.0159511280.21256351240.02173038430.1274834919

00.00507303960.01171313050000

0000.006236394500.0085731280

2.73749793882.08332937182.89891999392.31448041022.58054441752.72350114662.8027127294

9101268462665622395376

369339253209171233122

2333440702810050

2389422688714328

543512912587290

4274884015

9030208

35713272527310122285

211262011273

21581145411911911

7103903

11316709713810257

7815374327

0001010

2537218716551724151711921145

0.35869136780.57978966620.27915407850.38573085850.41001977590.33137583890.3283842795

0.14544737880.15500685870.15287009060.12122969840.11272247860.19546979870.1065502183

0.09184075680.01554641060.02416918430.04060324830.01845748190.08389261740.0436681223

0.09381158850.04298125290.13655589120.05104408350.04680290050.03607382550.0244541485

0.02128498230.0160036580.07794561930.00696055680.03823335530.06040268460.0786026201

0.00157666540.0123456790.02900302110.00464037120.002636783100.0131004367

0.00354749700.001812688800.001318391600.0069868996

0.14071738270.06035665290.04350453170.30568445480.20435069220.10234899330.2489082969

0.00827749310.00045724740.158308157100.00725115360.00167785230.0637554585

0.08474576270.0370370370.08761329310.02378190260.01252471980.09983221480.0096069869

0.00275916440.000457247400.00174013920.00593276200.0026200873

0.04454079620.076360310900.05626450120.09096901780.08557046980.0497816594

0.00275916440.0036579790.00906344410.00174013920.04878048780.00251677850.023580786

0000.000580046400.00083892620

0.53057091560.45594570930.51388538050.53012285180.52738162250.52803403740.5275634758

0.40455181890.41690583370.41422014960.36904562050.35498031530.46032793080.3441992441

0.31636584420.09339155860.12980513370.18767881260.10630864370.29994230960.1972609473

0.320281210.19514127730.39224813160.21908694590.20674049820.17289837410.1309220567

0.11821722360.09546909330.28694808690.04988339830.18004180210.2445851790.2884149265

0.01467703240.07826975310.1481373680.0359700420.022589335200.081933292

0.028873017400.016509340800.012613059200.0500341092

0.39810742290.24446517010.19675753230.52268523560.46814311080.33656762110.4993881446

0.05725202920.00507303960.420971864100.05153810890.01546840360.2531925194

0.30175550460.17610694450.30775977620.12827939340.07914467980.33187729870.0643831466

0.02345718180.005073039600.0159511280.043885117500.0224703128

0.19993155660.2833756500.23358945940.31461461180.303496480.2154670625

0.02345718180.02961037950.06150203840.0159511280.21256351240.02173038430.1274834919

0000.006236394500.0085731280

2.73749793882.07882744842.88874480212.31448041022.58054441752.72350114662.8027127294

naz

full

2853426615682186234215061173

1506799530914550807767

1029474377327222424187

113334288644830333184

124622616411534299

920685046147

10011178

0000000

164130714312789103141314

370162211223330

9012645941415525573

1901730142531

0201010

2447414363294112

117062011

00000100

6444251044432603

after half

4246814139203151

49776102314224

407703118016

3329722540

930121

1521005

122011

00000

128066174614

110020

73735363

01000

00000

010100

220400

00000

192117

k+half

431811524963332489

0800845

0400000

0300000

1300003

0000000

0000000

0000000

0000000

0300000

0000000

0100000

0000000

623086550

0000000

0000000

0000000

45

2895482315692227238917131329

1555880536924573949791

1069554377330233504203

1137420895455305356127

133652616411636300

2422785046152

22211189

0000000

165339020912799173601328

3810162211223530

9083036291415826176

1911730142531

437836525869833089

2448414364294112

1390102011

00000100

9927856861335794573848824488

s_t_r81

s_t_ree43

s_t_ro1

0.29162889090.56290849670.25582912110.38436313430.41634715930.35088078660.2961229947

0.15664349750.10270774980.08739605410.15947531930.09986057860.19438754610.1762477718

0.10768610860.0646591970.06147073210.05695547120.04060648310.10323637850.0452317291

0.11453611360.04901960780.14593184410.07852951330.05315440920.0729209340.0282976827

0.0133978040.00758636790.04255666070.01104590960.02021610320.0073740270.0668449198

0.00241764880.02649393090.00130441870.00862961680.00801673060.00020483410.0115864528

0.00221617810.00023342670.00016305230.00017259230.00017427680.00163867270.0020053476

0000000

0.16651556360.04551820730.0340779390.22074559890.15981178110.07374027040.2959001783

0.0038279440.00116713350.26447089520.00189851570.00383408850.0071691930.006684492

0.09146771430.03536414570.10255992170.02433551950.01010805160.0534616960.0169340463

0.0019139720.00011671340.00277188980.00517777010.00243987450.00512085210.0069073084

0.04402135590.09757236230.00081526170.04452882290.12164517250.06759524780.0198306595

0.00241764880.00560224090.00065220940.00241629270.06343673750.06022122080.0249554367

0.00130955980.001050420200.00172592340.000348553500.0024509804

000000.00204834080

0.5184562220.46666671950.50315130970.53021284910.52632156190.53016232220.5199124907

0.41893413870.33722888480.30730970030.42238552180.33193066390.45933627520.4413813621

0.34622117050.25546852610.24735555340.23545515690.18768909780.33819996620.2020284697

0.35805426990.2132596690.40519922720.2882520990.22503805860.27546051640.1455398571

0.08335925580.05342604710.19382308710.07180221160.11378332970.05223267860.2608982801

0.02101463780.13878035730.01249943220.05916886240.05581865350.00250988460.0745173121

0.01954161680.00281623310.0020515860.00215746360.00217607740.01516305870.0179717887

0000000

0.43065438450.20289342390.16613056960.48112461770.42279074940.27736690990.5198426201

0.03073538360.01137116560.50747181330.01716431410.03077584770.05107314110.0482952297

0.31561790870.17051066070.3369566260.13045767330.06699971640.22589440850.099638734

0.01728166380.00152482990.02354696640.03931715590.02117561570.0389666140.0495783155

0.1983449370.32758785210.00836495120.19989508320.36970997220.26273829180.11216466

0.02101463780.04190353090.00690192550.02100480610.25238544630.24411179130.1328752737

0.01254126430.010393716100.01584124240.004003601300.0212559445

000000.01829440490

2.79177149122.23383161612.7207627482.51423905712.61059839182.79151026332.6459003379

2895482315692227238917131329

1568889536934575949802

1069554377330233504203

1137420895455305356127

133652616411636300

2422785046152

22211189

165339020912799173601328

3810162211223530

9083036291415826176

1911730142531

437836525869833089

2448414364294112

00000100

9927856861335794573848824488

0.29162889090.56290849670.25582912110.38436313430.41634715930.35088078660.2961229947

0.15795305730.10375816990.08739605410.16120124270.10020913210.19438754610.1786987522

0.10768610860.0646591970.06147073210.05695547120.04060648310.10323637850.0452317291

0.11453611360.04901960780.14593184410.07852951330.05315440920.0729209340.0282976827

0.0133978040.00758636790.04255666070.01104590960.02021610320.0073740270.0668449198

0.00241764880.02649393090.00130441870.00862961680.00801673060.00020483410.0115864528

0.00221617810.00023342670.00016305230.00017259230.00017427680.00163867270.0020053476

0.16651556360.04551820730.0340779390.22074559890.15981178110.07374027040.2959001783

0.0038279440.00116713350.26447089520.00189851570.00383408850.0071691930.006684492

0.09146771430.03536414570.10255992170.02433551950.01010805160.0534616960.0169340463

0.0019139720.00011671340.00277188980.00517777010.00243987450.00512085210.0069073084

0.04402135590.09757236230.00081526170.04452882290.12164517250.06759524780.0198306595

0.00241764880.00560224090.00065220940.00241629270.06343673750.06022122080.0249554367

000000.00204834080

0.5184562220.46666671950.50315130970.53021284910.52632156190.53016232220.5199124907

0.42053931110.33915465750.30730970030.4244533870.33258550220.45933627520.4439589181

0.34622117050.25546852610.24735555340.23545515690.18768909780.33819996620.2020284697

0.35805426990.2132596690.40519922720.2882520990.22503805860.27546051640.1455398571

0.08335925580.05342604710.19382308710.07180221160.11378332970.05223267860.2608982801

0.02101463780.13878035730.01249943220.05916886240.05581865350.00250988460.0745173121

0.01954161680.00281623310.0020515860.00215746360.00217607740.01516305870.0179717887

0.43065438450.20289342390.16613056960.48112461770.42279074940.27736690990.5198426201

0.03073538360.01137116560.50747181330.01716431410.03077584770.05107314110.0482952297

0.31561790870.17051066070.3369566260.13045767330.06699971640.22589440850.099638734

0.01728166380.00152482990.02354696640.03931715590.02117561570.0389666140.0495783155

0.1983449370.32758785210.00836495120.19989508320.36970997220.26273829180.11216466

0.02101463780.04190353090.00690192550.02100480610.25238544630.24411179130.1328752737

000000.01829440490

2.78083539932.22536367272.7207627482.50046567992.60724962872.79151026332.6272219494

total

113221949361429543856465276324

5052320325583397221737122433

3111130187812826921792899

393115963369164013471837394

83039412133528729681216

92527351102221128156

13718786354781

4000000

528418868984861375519354891

167495773367082632

3257120525945223011112254

15713447910645128

1731272543159125721277713

92229114531054461361

36314203026

720140481

35210326722405923498218091997118509

s_t_r39

s_t_ree14

s_t_ro0

0.3215563760.59662708130.2552890810.40611966980.39268192030.32682389460.3416716192

0.14348196540.09803501470.10632195850.14456549490.10165527990.18586951080.1314495651

0.08835558080.03982002940.03649361990.05455783470.03173001970.08973010870.0485709655

0.11164441920.04884916750.14003075770.06979317390.06176349210.09198337590.0212869415

0.02357284860.01205925560.05041772310.01497999830.03998349310.04847028190.0656977687

0.00261289410.01613001960.0145891350.0043407950.01013343120.00640929350.0084283322

0.00389094010.00055093050.003242030.00025534090.0016048420.00235341240.0043762494

0.0001136041000000

0.15007100260.05772526930.03732490960.20686866970.17217662430.09689049120.2642498244

0.00474297070.00149975510.23995178520.00153204530.00320968410.00410595360.0341455508

0.09250213010.03688173360.10781828010.02221465660.01380164150.05568073710.0137230536

0.00445896050.00039789420.00182883740.00336198830.00486037870.00225326720.0069155546

0.04916216980.08340475020.0017872730.067707890.11793296350.06394271690.0385218002

0.00261289410.00700905970.00473835160.00225551110.04832867160.0230834710.0195040251

0.00102243680.00094882470.00016625790.00085113630.000137557900.001404722

0.00019880720.000061214500.000595795400.00240348510.0000540278

0.52634161160.44454602140.50286747740.52796498910.52955784750.5273024530.52935788

0.40190140490.32847210750.34379083120.40336734450.33528380980.45122387970.3848079184

0.30929179660.18517754770.17430126250.22892848270.15795228480.31210500950.2119521347

0.35313319120.21276363410.39715304290.26805954590.24811023940.31665121170.1182252785

0.12745202970.07686226250.21729661650.09079105430.18570140130.21165788060.2580616117

0.02241898550.09603987870.08897857790.03406579920.06713128020.046695670.0580757356

0.03114956480.00596428620.02680797930.00304756690.01489831510.02054771490.0342926812

0.0014886336000000

0.41063671140.23751946370.1770588240.47025653470.43699095430.3262788360.5073664229

0.03661570250.01406928890.49410476850.01432512180.02658694620.03255227530.1663625385

0.31768650370.17559207920.34645531430.12201054350.08528056830.23200369550.0849080274

0.03482036540.00449434550.01663301580.02762367430.03735062810.01981470450.0496256002

0.21367391230.2988998250.0163142710.26301348090.36370066840.25366562690.1809823923

0.02241898550.05016078020.03658670310.01983119770.21124350490.125504740.1107845067

0.01015665480.00952769030.00208725040.00868016190.001764547700.013310443

0.00244460090.000856743800.006382693700.02091189770.0007658944

2.82163065442.14094595472.84043593462.48834819112.70155299592.89691559542.7088790654

113221949361429543856465276324

5088323425623417222037122459

3111130187812826921792899

393115963369164013471837394

83039412133528729681216

92527351102221128156

13718786354781

528418868984861375519354891

167495773367082632

3257120525945223011112254

15713447910645128

1731272543159125721277713

92229114531054461361

720140481

35206326722405923498218091997118509

0.32159291030.59662708130.2552890810.40611966980.39268192030.32682389460.3416716192

0.14452082030.09898383940.10648821650.14541663120.10179283780.18586951080.1328542871

0.08836561950.03982002940.03649361990.05455783470.03173001970.08973010870.0485709655

0.11165710390.04884916750.14003075770.06979317390.06176349210.09198337590.0212869415

0.02357552690.01205925560.05041772310.01497999830.03998349310.04847028190.0656977687

0.00261319090.01613001960.0145891350.0043407950.01013343120.00640929350.0084283322

0.00389138220.00055093050.003242030.00025534090.0016048420.00235341240.0043762494

0.15008805320.05772526930.03732490960.20686866970.17217662430.09689049120.2642498244

0.00474350960.00149975510.23995178520.00153204530.00320968410.00410595360.0341455508

0.09251263990.03688173360.10781828010.02221465660.01380164150.05568073710.0137230536

0.00445946710.00039789420.00182883740.00336198830.00486037870.00225326720.0069155546

0.04916775550.08340475020.0017872730.067707890.11793296350.06394271690.0385218002

0.00261319090.00700905970.00473835160.00225551110.04832867160.0230834710.0195040251

0.00019882970.000061214500.000595795400.00240348510.0000540278

0.52634870210.44454602140.50286747740.52796498910.52955784750.5273024530.52935788

0.4033071350.3302757330.34408837740.40451065130.33553892090.45122387970.3868827524

0.30931245380.18517754770.17430126250.22892848270.15795228480.31210500950.2119521347

0.3531550120.21276363410.39715304290.26805954590.24811023940.31665121170.1182252785

0.12746264630.07686226250.21729661650.09079105430.18570140130.21165788060.2580616117

0.02242110440.09603987870.08897857790.03406579920.06713128020.046695670.0580757356

0.03115246610.00596428620.02680797930.00304756690.01489831510.02054771490.0342926812

0.41065876650.23751946370.1770588240.47025653470.43699095430.3262788360.5073664229

0.03661908510.01406928890.49410476850.01432512180.02658694620.03255227530.1663625385

0.3177074350.17559207920.34645531430.12201054350.08528056830.23200369550.0849080274

0.03482359070.00449434550.01663301580.02762367430.03735062810.01981470450.0496256002

0.21369013040.2988998250.0163142710.26301348090.36370066840.25366562690.1809823923

0.02242110440.05016078020.03658670310.01983119770.21124350490.125504740.1107845067

0.00244484610.000856743800.006382693700.02091189770.0007658944

2.81152447782.13322188992.83864623052.4808113362.70004355932.89691559542.6976434563

maxmin

total2.81152447782.13322188992.83864623052.4808113362.70004355932.89691559542.69764345632.89691559542.1332218899

sam2.79984089132.15018938682.70601525142.47641893682.60015519992.70273005192.63170707372.79984089132.1501893868

poe2.85414306892.08079698572.92794512432.41654029752.8608884872.86996946152.64720238272.92794512432.0807969857

chee2.78916801271.77956488942.86292129062.41030877762.64898416052.82229453762.87997775452.87997775451.7795648894

tanav2.69467840312.00842400792.66918529542.47445619012.60708259292.80761472322.40063555832.80761472322.0084240079

katha2.73749793882.07882744842.88874480212.31448041022.58054441752.72350114662.80271272942.88874480212.0788274484

naz2.78083539932.22536367272.7207627482.50046567992.60724962872.79151026332.62722194942.79151026332.2253636727

Text 12.78916801271.77956488942.86292129062.41030877762.64898416052.82229453762.8799777545

Text 22.73749793882.07882744842.88874480212.31448041022.58054441752.72350114662.8027127294

Text 32.79984089132.15018938682.70601525142.47641893682.60015519992.70273005192.6317070737

Text 42.78083539932.22536367272.7207627482.50046567992.60724962872.79151026332.6272219494

Text 52.85414306892.08079698572.92794512432.41654029752.8608884872.86996946152.6472023827

Text 62.81152447782.13322188992.83864623052.4808113362.70004355932.89691559542.6976434563

Tanav se Mukti2.69467840312.00842400792.66918529542.47445619012.60708259292.80761472322.4006355583

parametersabcNa/N1bc

Text 12049.920.9035-0.0329cheeleText 1181620.11286862680.03290.9035

Text 22797.6550.9155-0.149kataaText 2223750.12503486030.1490.9155

Text 39277.99150.921597-0.209samText 3706220.13137537170.2090.921597

Text 410919.5820.9152-0.178nazText 4828030.13187423160.1780.9152

Text 59744.1690.896230.042poemText 5909040.1071918617-0.0420.89623

Text 639394.760.907-0.0865totalText 63259790.12085060690.08650.907

Tanav5072.3730.896-0.0382tanavTanav411140.12337337650.03820.896

parametersabcNa/N2bc

Text 11106.2420.943-0.332cheeleText 182980.13331429260.3320.943

Text 21497.5960.959-0.501kataaText 298310.15233404540.5010.959

Text 35277.070.971-0.658samText 3296230.17814097150.6580.971

Text 46226.2990.962-0.621nazText 4344040.18097602020.6210.962

Text 55668.7170.927-0.276poemText 5402170.14095325360.2760.927

Text 622591.7340.952-0.498totalText 61391710.16233075860.4980.952

Tanav2982.1190.936-0.459tanavTanav167980.17752821760.4590.936

total

2.78916801272.73749793882.79984089132.78083539932.85414306892.81152447782.6946784031

1.77956488942.07882744842.15018938682.22536367272.08079698572.13322188992.0084240079

2.86292129062.88874480212.70601525142.7207627482.92794512432.83864623052.6691852954

2.41030877762.31448041022.47641893682.50046567992.41654029752.4808113362.4744561901

2.64898416052.58054441752.60015519992.60724962872.8608884872.70004355932.6070825929

2.82229453762.72350114662.70273005192.79151026332.86996946152.89691559542.8076147232

2.87997775452.80271272942.63170707372.62722194942.64720238272.69764345632.4006355583

Text 1

Text 2

Text 3

Text 4

Text 5

Text 6

Tanav se Mukti

letters

entropy

Sheet3

a/N1

b

c

a/N2

b

c

a/N2

b

c

_1296182662.unknown

_1296182663.unknown

_1296182572.unknown

_1295003451.xls

Chart3

0.11286862680.03290.9035

Hemlata

Documents

Transcript of Hemlata