Re: st: Re:Interesting results from a simulation

[Marcello Pagano <pagano@hsph.harvard.edu>]

At first glance, is this not another instance of Zipf's law?

m.p.

On 3/20/2011 4:18 PM, Victor Zammit wrote:
> Dear Statalisters,
>
> I have simulated drawing at random,one observation with replacement,at 
> a time ,for 30,000 times, from a finite population of 30,000 
> observations.The same process was repeated 200 times.Then I made a 
> count for every observation and discovered that any given 
> observation,after 30000 trials has the probability of realising 0 
> times(c0) is ~36.756%,the probability of realing 1 time (c1) is 
> ~36.83% ,the probability of realing 2 times (c2) is 1/2 as much,i.e. 
> ~18.4%.That of realising 3 time (c3) is about 1/3 of 18.4 = ~6.11%.and 
> the pattern basically continues,as the summation at the 
> bottom,demonstrates.
>
>
>
> c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 n
>
> 11018 11054 5549 1807 450 107 13 2 0 0 0 1
>
> 11133 10980 5403 1884 471 102 21 6 0 0 0 2
>
> 11018 11054 5549 1807 450 107 13 2 0 0 0 3
>
> .................................................................................................................................................................................... 
>
>
> 10886 11273 5482 1797 453 97 11 0 0 1 0 134
>
> 11026 11013 5554 1847 472 78 10 0 0 0 0 135
>
> 11019 11030 5574 1805 465 96 10 1 0 0 0 136
>
> ...................................................................................................................................................................................... 
>
>
> 11037 10981 5610 1823 443 86 13 6 1 0 0 199
>
> 11011 11032 5583 1827 439 85 21 2 0 0 0 200
>
> PS If anyone is interested I would provide the complete dataset.Please 
> let me know.
>
> . summ
>
> Variable Obs Mean Std. Dev. Min Max
>
>
> c0 200 11026.87 61.53633 10886 11184
>
> c1 200 11050.32 82.50102 10839 11273
>
> c2 200 5520.295 69.39095 5366 5672
>
> c3 200 1834.235 40.62328 1761 1930
>
> c4 200 457.595 15.43835 415 502
>
>
> c5 200 91.255 10.32536 72 117
>
> c6 200 16.56 4.544188 7 25
>
> c7 200 2.675 2.039651 0 7
>
> c8 200 .195 .3971949 0 1
>
> c9 200 .01 .0997484 0 1
>
>
> c10 200 0 0 0 0
>
> Dividing the above variables c0-c10 by 30000 to get the respective 
> probabilities and then summ. results in:
>
> . summ
>
> Variable Obs Mean Std. Dev. Min Max
>
>
> c0 200 .3675622 .0020512 .3628667 .3728
>
> c1 200 .3683438 .00275 .3613 .3757667
>
> c2 200 .1840098 .002313 .1788667 .1890667
>
> c3 200 .0611412 .0013541 .0587 .0643333
>
> c4 200 .0152532 .0005146 .0138333 .0167333
>
>
> c5 200 .0030418 .0003442 .0024 .0039
>
> c6 200 .000552 .0001515 .0002333 .0008333
>
> c7 200 .0000892 .000068 0 .0002333
>
> c8 200 6.50e-06 .0000132 0 .0000333
>
> c9 200 3.33e-07 3.32e-06 0 .0000333
>
>
> c10 200 0 0 0 0
>
> Note:the most number of times that a given observation is drawn in one 
> set of 30000 draws is 9,and in my experiment happened in the 134th loop.
>
> I find,the probability pattern,quite surprising.Can anyone provide any 
> intuition on this ? Why is the probability of an observation not 
> realising ,equal
>
> to that of realising just once,(= ~.368),in the number of trials the 
> size of the population ?
>
> Victor Zammit.
>
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