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I have a discrete frequency distribution, that looks like this

Frequency Distribution

I am trying to find what type of distribution is it?

I looked at many models but it does not seem to comply with any.

I have 345 samples, each has a frequency. The top 20 frequencies sum is greater than the sum of the remaining 325.

Update: Here is log-log plot

Log-Log

Preto Chart Preto

Data Sample Rank Frequency 1 11283380 2 10746051 3 9880160 4 7088819 5 6083811 6 5880305 7 5162758 8 5112340 9 4790522 10 4757319 11 4704226 12 4656856 13 4602855 14 4443199 15 3920582 16 3873183 17 3701584 18 3616144 19 3595352 20 3455586 21 3454769 22 3447600 23 3176357 24 2953578 25 2685691 26 2538326 27 2517904 28 2361178 29 2321718 30 2298187 31 2107593 32 2099459 33 2067878 34 2065825 35 2038860 36 2019911 37 1891243 38 1840260 39 1817637 40 1758235 41 1657344 42 1651883 43 1449834 44 1425727 45 1421574 46 1419489 47 1393750 48 1365944 49 1333684 50 1313764 51 1116110 52 1018205 53 933583 54 912332 55 904322 56 894303 57 892826 58 859628 59 847616 60 821070 61 811475 62 795705 63 782508 64 753768 65 746363 66 730726 67 712801 68 712707 69 705775 70 685044 71 680739 72 674921 73 648874 74 618832 75 595568 76 576773 77 503718 78 476542 79 461991 80 420085 81 418143 82 406194 83 399628 84 389467 85 371231 86 360972 87 355256 88 333312 89 329501 90 305836 91 304731 92 302782 93 293852 94 286274 95 283938 96 280961 97 279916 98 274902 99 274189 100 268081 101 260194 102 257674 103 256995 104 247407 105 237400 106 229708 107 226061 108 219854 109 218018 110 216291 111 216273 112 211697 113 206972 114 204153 115 195442 116 187550 117 184599 118 170596 119 165042 120 159314 121 151599 122 149400 123 149027 124 148454 125 147450 126 140889 127 138447 128 135733 129 132508 130 132454 131 131411 132 129300 133 128163 134 125816 135 125192 136 121761 137 121145 138 120907 139 119436 140 118433 141 117280 142 116796 143 111973 144 111952 145 108356 146 104955 147 103942 148 103926 149 102907 150 102593 151 102417 152 101877 153 101791 154 100472 155 100288 156 100113 157 99886 158 97052 159 92872 160 92184 161 89339 162 89162 163 88933 164 87373 165 84388 166 83532 167 82868 168 82654 169 81812 170 75932 171 71633 172 70269 173 67750 174 67559 175 66874 176 66612 177 65156 178 59972 179 58490 180 57894 181 56471 182 51145 183 50960 184 49638 185 49298 186 48752 187 48623 188 48569 189 48539 190 48476 191 47581 192 46281 193 45200 194 43946 195 43168 196 42729 197 42703 198 41507 199 41496 200 38928 201 38680 202 36862 203 36491 204 36234 205 35958 206 34705 207 34688 208 34061 209 33734 210 33018 211 32867 212 32700 213 32654 214 32342 215 31930 216 31621 217 31415 218 31403 219 30307 220 29358 221 29304 222 29049 223 27409 224 27165 225 26645 226 26499 227 26301 228 26184 229 25632 230 24927 231 24889 232 24826 233 24601 234 24439 235 24177 236 23539 237 23144 238 22564 239 22322 240 22267 241 21299 242 20884 243 20600 244 20439 245 19964 246 19680 247 18150 248 17424 249 17321 250 16927 251 16881 252 16442 253 15598 254 15520 255 15335 256 15177 257 14933 258 14303 259 13886 260 13870 261 13770 262 13462 263 13437 264 13233 265 13231 266 13206 267 13170 268 12991 269 12597 270 12583 271 12501 272 12438 273 11830 274 11757 275 11507 276 10953 277 10796 278 10792 279 10687 280 10251 281 9653 282 9538 283 8614 284 8232 285 8008 286 7916 287 7192 288 6956 289 6583 290 6469 291 6308 292 5691 293 5439 294 5251 295 4724 296 4208 297 3760 298 3692 299 3601 300 3555 301 3359 302 3332 303 3317 304 3267 305 3213 306 3188 307 3171 308 3075 309 2506 310 2097 311 2026 312 1756 313 1495 314 1491 315 1476 316 1283 317 1281 318 1165 319 1108 320 1032 321 970 322 821 323 796 324 780 325 729 326 616 327 549 328 538 329 536 330 535 331 533 332 375 333 250 334 176 335 14 336 7 337 5 338 4 339 3 340 3 341 2 342 2 343 1 344 1 345 1

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  • $\begingroup$ It looks like a rank-size distribution. $\endgroup$ – user2974951 Sep 26 '18 at 6:07
  • $\begingroup$ Actually rank-size must show a linear graph when a log-log plot is plotted This one shows a curved line concaved to the origin. $\endgroup$ – Ahmad Hajjar Sep 26 '18 at 9:30
  • $\begingroup$ @AhmadHajjar Hi and welcome. 1) Please do post your log-log plot. 2) Please do post your Pareto fit. $\endgroup$ – Jim Sep 26 '18 at 9:50
  • $\begingroup$ Hi @Jim, Thank you for commenting ... I updated the question :) $\endgroup$ – Ahmad Hajjar Sep 26 '18 at 10:09
  • $\begingroup$ Hi @Jim I also added preto $\endgroup$ – Ahmad Hajjar Sep 26 '18 at 11:50
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Is this not just a Gamma distribution with a small k?

https://en.wikipedia.org/wiki/Gamma_distribution

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  • $\begingroup$ I thought so but shouldn't the variable be continuous ? $\endgroup$ – Ahmad Hajjar Sep 26 '18 at 5:27
  • $\begingroup$ thank you very much for bringing it up :D because I looked for analogue of gamma distribution for discrete variables, and found what I was looking for "Negative binomial distribution" $\endgroup$ – Ahmad Hajjar Sep 26 '18 at 5:32
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It looks like a Pareto distribution to me. If you have the data used to create the plots you provided, you can try some curve fitting and see for yourself. In short, you want to find the goodness of fit for your observed data and the suspected distribution.

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  • $\begingroup$ I dont think it is zeta distribution, if you look at the log-log plot I provided it shows a curve .. it does not show a linear relationship $\endgroup$ – Ahmad Hajjar Sep 27 '18 at 3:52
  • $\begingroup$ @AhmadHajjar Thanks, it certainly looks like belonging to the power-law family. If you dump your data in an simple excel sheet it's not too hard to do the curve fitting - in case you want to be more confident. $\endgroup$ – Michael Sep 27 '18 at 8:47

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