Statistical Distributions of English Text

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Statistical Distributions of English Text

Contents

First-Order Statistics
Second-Order Statistics
Third-Order Statistics
Notes

I. First-Order Statistics

|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|
|    a    |    b    |    c    |    d    |    e    |    f    |    g    |    h    |    i    |    j    |    k    |    l    |    m    |    n    |    o    |    p    |    q    |    r    |    s    |    t    |    u    |    v    |    w    |    x    |    y    |    z    |  SPACE  |
|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|
 0.0651738 0.0124248 0.0217339 0.0349835 0.1041442 0.0197881 0.0158610 0.0492888 0.0558094 0.0009033 0.0050529 0.0331490 0.0202124 0.0564513 0.0596302 0.0137645 0.0008606 0.0497563 0.0515760 0.0729357 0.0225134 0.0082903 0.0171272 0.0013692 0.0145984 0.0007836 0.1918182

II. Second-Order Statistics

The second number in the first row is the conditional probability P(X_i=b|X_i-1=a)=0.0228302

     ||=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|
     ||    a    |    b    |    c    |    d    |    e    |    f    |    g    |    h    |    i    |    j    |    k    |    l    |    m    |    n    |    o    |    p    |    q    |    r    |    s    |    t    |    u    |    v    |    w    |    x    |    y    |    z    |  SPACE  |
     ||=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|
a    ||0.0002835 0.0228302 0.0369041 0.0426290 0.0012216 0.0075739 0.0171385 0.0014659 0.0372661 0.0002353 0.0110124 0.0778259 0.0260757 0.2145354 0.0005459 0.0195213 0.0001749 0.1104770 0.0934290 0.1317960 0.0098029 0.0306574 0.0088799 0.0009562 0.0233701 0.0018701 0.0715219 
b    ||0.0580027 0.0058699 0.0000791 0.0022625 0.3416714 0.0002057 0.0004272 0.0003639 0.0479084 0.0076894 0.0000000 0.1150560 0.0012816 0.0003481 0.0966553 0.0000158 0.0000000 0.0740301 0.0226884 0.0107430 0.1196127 0.0011550 0.0000316 0.0000000 0.0864502 0.0000000 0.0074521 
c    ||0.1229841 0.0000271 0.0215451 0.0005246 0.1715916 0.0000090 0.0000000 0.1701716 0.0565490 0.0000000 0.0453966 0.0488879 0.0000000 0.0000362 0.1759242 0.0000090 0.0017185 0.0376812 0.0010492 0.0906756 0.0358361 0.0000000 0.0000000 0.0000000 0.0041969 0.0000090 0.0151774 
d    ||0.0280345 0.0005057 0.0002585 0.0081086 0.1224833 0.0006799 0.0054844 0.0007080 0.0794902 0.0003484 0.0001911 0.0092662 0.0021466 0.0030456 0.0397283 0.0001630 0.0000225 0.0178918 0.0307037 0.0009159 0.0178805 0.0027759 0.0013655 0.0000000 0.0076478 0.0000000 0.6201541 
e    ||0.0545873 0.0012798 0.0224322 0.0843434 0.0317097 0.0085640 0.0052834 0.0017762 0.0127186 0.0002605 0.0010967 0.0339975 0.0186268 0.0815271 0.0032334 0.0101307 0.0021424 0.1307517 0.0712793 0.0241537 0.0014289 0.0157312 0.0070879 0.0105139 0.0125997 0.0001831 0.3525610 
f    ||0.0638579 0.0002384 0.0003179 0.0002086 0.0928264 0.0500293 0.0000199 0.0000993 0.0820576 0.0000000 0.0000199 0.0266638 0.0000397 0.0000894 0.1545186 0.0001689 0.0000099 0.0825344 0.0039539 0.0341940 0.0334986 0.0000099 0.0001987 0.0000000 0.0015200 0.0000000 0.3729250 
g    ||0.0592435 0.0003842 0.0005205 0.0020078 0.1482326 0.0002727 0.0101631 0.1420108 0.0501091 0.0000248 0.0000372 0.0395122 0.0029870 0.0127906 0.0573224 0.0005577 0.0000000 0.0884686 0.0261142 0.0062466 0.0256309 0.0000372 0.0003470 0.0000000 0.0032720 0.0001363 0.3235710 
h    ||0.1580232 0.0007737 0.0020460 0.0005185 0.4597035 0.0004627 0.0000359 0.0000718 0.1252667 0.0000000 0.0000040 0.0014278 0.0013042 0.0012922 0.0700557 0.0000439 0.0003191 0.0117178 0.0022056 0.0297253 0.0131497 0.0000000 0.0010290 0.0000000 0.0072309 0.0000000 0.1135928 
i    ||0.0166996 0.0069144 0.0486793 0.0363474 0.0480664 0.0271435 0.0307856 0.0000775 0.0004826 0.0000035 0.0073125 0.0526842 0.0412929 0.2618995 0.0497818 0.0062698 0.0004333 0.0437620 0.1157982 0.1198384 0.0007010 0.0235788 0.0000211 0.0018810 0.0000000 0.0032265 0.0563193 
j    ||0.2106638 0.0000000 0.0000000 0.0000000 0.1906420 0.0000000 0.0000000 0.0000000 0.0004353 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.2644178 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.3299238 0.0000000 0.0000000 0.0000000 0.0002176 0.0000000 0.0036997 
k    ||0.0169234 0.0011671 0.0005058 0.0017118 0.3321662 0.0041628 0.0004669 0.0007781 0.1300965 0.0000000 0.0003112 0.0185963 0.0009726 0.1009570 0.0113601 0.0012060 0.0000000 0.0004279 0.0613523 0.0022954 0.0029956 0.0000000 0.0041239 0.0000000 0.0086757 0.0000000 0.2987473 
l    ||0.1016800 0.0005515 0.0020459 0.0668636 0.1657445 0.0134024 0.0011801 0.0001542 0.1107889 0.0000119 0.0053728 0.1355180 0.0055389 0.0009726 0.0826499 0.0022654 0.0000059 0.0018443 0.0230153 0.0180635 0.0144461 0.0041630 0.0025797 0.0000000 0.0968765 0.0000237 0.1442414 
m    ||0.1539307 0.0285939 0.0001653 0.0025384 0.2496134 0.0017798 0.0000195 0.0003015 0.0877464 0.0000195 0.0000000 0.0015756 0.0221846 0.0029567 0.1098532 0.0485124 0.0000000 0.0169910 0.0249954 0.0008461 0.0385435 0.0000292 0.0001167 0.0000000 0.0505257 0.0000000 0.1581614 
n    ||0.0240107 0.0005432 0.0423173 0.1767352 0.0849166 0.0053036 0.1188694 0.0028799 0.0295789 0.0012223 0.0071353 0.0087755 0.0006582 0.0085073 0.0653564 0.0003343 0.0009716 0.0004144 0.0427003 0.0956004 0.0093814 0.0033500 0.0008497 0.0003343 0.0121150 0.0001288 0.2570099 
o    ||0.0083175 0.0072923 0.0127087 0.0203076 0.0029439 0.1135873 0.0060659 0.0018527 0.0087857 0.0001978 0.0106912 0.0268647 0.0580447 0.1459838 0.0330625 0.0138659 0.0002308 0.1175433 0.0322680 0.0492657 0.1337201 0.0164801 0.0488371 0.0005374 0.0033923 0.0008571 0.1262960 
p    ||0.1284508 0.0004427 0.0004427 0.0004713 0.2213542 0.0001428 0.0000857 0.0221226 0.0538854 0.0000286 0.0001143 0.0957597 0.0010854 0.0005856 0.1212242 0.0607692 0.0000000 0.1362487 0.0222939 0.0408603 0.0270926 0.0000000 0.0011711 0.0000000 0.0042274 0.0000000 0.0611405 
q    ||0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0002284 0.0002284 0.0000000 0.9949749 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0045683 
r    ||0.0733524 0.0032081 0.0116789 0.0284070 0.2345530 0.0056616 0.0107385 0.0026432 0.0792432 0.0000435 0.0087196 0.0117263 0.0192448 0.0221961 0.0919374 0.0048043 0.0000316 0.0189406 0.0459213 0.0421561 0.0173721 0.0070603 0.0019873 0.0000040 0.0284504 0.0055945 0.2243241 
s    ||0.0349781 0.0006441 0.0157796 0.0015208 0.1179849 0.0010558 0.0004688 0.0569819 0.0506053 0.0000495 0.0053780 0.0114497 0.0065520 0.0022488 0.0491264 0.0287844 0.0008309 0.0001906 0.0463897 0.1269191 0.0330152 0.0000800 0.0053856 0.0000000 0.0020925 0.0000000 0.4014880 
t    ||0.0393295 0.0001590 0.0037195 0.0000674 0.0892434 0.0009218 0.0000404 0.3352928 0.0666758 0.0000054 0.0000162 0.0146273 0.0009110 0.0011051 0.0913053 0.0000809 0.0000027 0.0310281 0.0245378 0.0171177 0.0185732 0.0000027 0.0078702 0.0000000 0.0121422 0.0002776 0.2449470 
u    ||0.0261517 0.0181796 0.0459729 0.0223272 0.0308931 0.0058765 0.0505571 0.0000699 0.0298191 0.0000087 0.0001572 0.1066327 0.0308669 0.1156002 0.0020170 0.0448465 0.0001746 0.1626908 0.1207345 0.1249869 0.0000349 0.0009343 0.0002008 0.0008819 0.0002969 0.0010042 0.0580839 
v    ||0.1022242 0.0000000 0.0000000 0.0049559 0.6796927 0.0000000 0.0000000 0.0002371 0.1467561 0.0000000 0.0000000 0.0001423 0.0000000 0.0128284 0.0429195 0.0000000 0.0000000 0.0008299 0.0003083 0.0000000 0.0025847 0.0005928 0.0000000 0.0000000 0.0038888 0.0000000 0.0020393 
w    ||0.1832539 0.0003329 0.0002984 0.0018938 0.1605624 0.0013085 0.0000344 0.1893372 0.1788924 0.0000000 0.0005050 0.0089412 0.0002755 0.0372798 0.0933831 0.0000803 0.0000115 0.0082066 0.0126485 0.0018135 0.0011707 0.0000000 0.0003214 0.0000000 0.0006887 0.0000000 0.1187604 
x    ||0.0600144 0.0000000 0.1573582 0.0010050 0.0554200 0.0000000 0.0001436 0.0132089 0.1122757 0.0000000 0.0000000 0.0014358 0.0001436 0.0000000 0.0055994 0.2157933 0.0031587 0.0000000 0.0027279 0.2360373 0.0195262 0.0051687 0.0001436 0.0093324 0.0020101 0.0000000 0.0994975 
y    ||0.0072178 0.0039321 0.0011985 0.0020738 0.0562745 0.0015217 0.0003097 0.0007137 0.0141393 0.0000135 0.0000269 0.0031914 0.0039051 0.0022488 0.1205478 0.0027875 0.0000000 0.0048882 0.0324935 0.0109613 0.0005925 0.0000673 0.0016025 0.0001347 0.0000943 0.0002020 0.7288617 
z    ||0.4219769 0.0007526 0.0060211 0.0067737 0.3038133 0.0000000 0.0000000 0.0005018 0.0709985 0.0002509 0.0000000 0.0198194 0.0000000 0.0000000 0.0730055 0.0000000 0.0000000 0.0002509 0.0017561 0.0005018 0.0037632 0.0010035 0.0000000 0.0000000 0.0100351 0.0268440 0.0519318 
SPACE||0.1062437 0.0444502 0.0391600 0.0282947 0.0213084 0.0400793 0.0171783 0.0606047 0.0678165 0.0034660 0.0045451 0.0243019 0.0406429 0.0234882 0.0649920 0.0273498 0.0022208 0.0214068 0.0704687 0.1460781 0.0092399 0.0079497 0.0606385 0.0001107 0.0114638 0.0002911 0.0562102 
     ||=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|

III. Third-Order Statistics

The fourth number in the second row is the conditional probability P(X_i=d|X_i-1=b,X_i-2=a)=0.0085877
For brevity, we include only the first 5 rows.

The entire matrix (729 rows x 27 columns) can be downloaded from the third-order statistic file.

     ||=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|
     ||    a    |    b    |    c    |    d    |    e    |    f    |    g    |    h    |    i    |    j    |    k    |    l    |    m    |    n    |    o    |    p    |    q    |    r    |    s    |    t    |    u    |    v    |    w    |    x    |    y    |    z    |    S    |
     ||=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|
a a  ||0.0000000 0.0000000 0.0106383 0.3297872 0.0000000 0.0106383 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0212766 0.4361702 0.1063830 0.0000000 0.0000000 0.0000000 0.0425532 0.0106383 0.0000000 0.0106383 0.0000000 0.0106383 0.0000000 0.0000000 0.0000000 0.0106383 
a b  ||0.0075307 0.0140045 0.0000000 0.0085877 0.0202140 0.0000000 0.0000000 0.0029066 0.1762452 0.0014533 0.0000000 0.4001850 0.0000000 0.0019818 0.2522130 0.0000000 0.0000000 0.0146651 0.0622275 0.0000000 0.0192892 0.0000000 0.0000000 0.0000000 0.0085877 0.0000000 0.0099088 
a c  ||0.0066204 0.0000817 0.0963629 0.0006539 0.2368615 0.0000000 0.0000000 0.1985288 0.0402942 0.0000000 0.1439313 0.0111157 0.0000000 0.0001635 0.0089089 0.0000000 0.0155292 0.0263997 0.0003269 0.1977115 0.0092358 0.0000000 0.0000000 0.0000000 0.0048222 0.0000000 0.0024520 
a d  ||0.0304960 0.0001415 0.0000708 0.0352367 0.1144131 0.0038916 0.0004245 0.0027595 0.0417463 0.0038916 0.0000000 0.0098351 0.0241987 0.0031840 0.0245525 0.0000000 0.0000708 0.0103304 0.0175476 0.0022642 0.0116040 0.0342461 0.0005661 0.0000000 0.0419585 0.0000000 0.5865704 
a e  ||0.0345679 0.0000000 0.0024691 0.0098765 0.0074074 0.0000000 0.0222222 0.0000000 0.0000000 0.0000000 0.0000000 0.1753086 0.0024691 0.0123457 0.1135802 0.0000000 0.0049383 0.0839506 0.0074074 0.0049383 0.0246914 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4938272 
     ||=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|=========|

IV. Notes

The above statistics are derived from these classics:
1. Origin of Species (Charles Darwin)
2. The Voyage of the Beagle (Charles Darwin)
3. Jane Eyre (Charlotte Bronte)
4. Wuthering Heights (Emily Bronte)
5. Tarzan of the Apes (Edgar Rice Burroughs)
6. The Return of Tarzan (Edgar Rice Burroughs)
7. Paradise Lost (John Milton)
All of these are available at www.literature.org.
All upper-case letters were converted to lower-case.
All numbers and all special characters were removed.
A carriage return is treated as a space.
There are exactly 5086936 characters in these files.
The first-order statistics are comparable with Table 2.1 in Blahut's Information Theory book.
Unless every elements of a row are zeros, the row sum should be approximately one. There may be round-off errors.

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