> From: Oleg Kobchenko <[EMAIL PROTECTED]>
>
> > From: Brian Schott
> >
> > The poisson distribution is almost identical to the
> > normal distribution when its parameter is 15 or larger, so
> > you may want to use the normal distribution. More
> > specifically, according to George Fishman, as the mean,
> > lambda, increases the distribution of
> > (X-lambda)/sqrt(lambda) converges to the standard normal
> > distribution (ie mean 0, std dev 1); if Y is from standard
> > normal then
> >
> > X=max(0,integer [lambda+Y*sqrt(lambda)+0.5])
> >
> > A key feature would be to generate the poisson
> > cumulative probabilities only one time as you did in your
> > revised approach, whether you use the Poisson or the normal
> > approximation. If the mean of the Poisson does not vary,
> > then why not generate all 1 000 000 at once?
> >
> > It seems to me that you could generate 1000000
> > Poisson and uniform variates all at one time (in an array of
> > shape 500 2000?) and then focus on keeping track of the
> > (ending) inventory level (i) in your main process using J's
> > strength of array processing. This is the challenging part,
> > imo, especially avoiding the for. for iteration.
>
> dstat poissonrand 100 10000
> sample size: 10000
> minimum: 64
> maximum: 141
> median: 100
> mean: 100.006
> std devn: 10.0345
> skewness: 0.12287
> kurtosis: 3.03206
> dstat <.100+10*normalrand 10000
> sample size: 10000
> minimum: 61
> maximum: 137
> median: 99
> mean: 99.3547
> std devn: 10.0235
> skewness: 0.0298283
> kurtosis: 3.0363
>
> 3 ts '$<.100+10*normalrand 10000'
> 0.00326381 1.31347e6
> 3 ts '$poissonrand 100 10000'
> 0.513158 690880
You could compare the two samples, visually it
is strikingly close.
load 'stats plot'
plots=: 4 : 0
pd 'reset'
pd (~. ; #/.~) /:~ poissonrand x , y
pd (~. ; #/.~) /:~ <.0.5+x+(%:x)*normalrand y
pd 'show'
)
100 plots 10000
BTW, is there a library for J to do parametric or non-parametric
sample comparisons?
The closest I got is:
N regression & (/:~) P
Var. Coeff. S.E. t
0 1.18791 0.05245 22.65
1 0.99323 0.00052 1892.61
Source D.F. S.S. M.S. F
Regression 1 978915.01515 978915.01515 3581955.71
Error 9998 2732.35995 0.27329
Total 9999 981647.37510
S.E. of estimate 0.52277
Corr. coeff. squared 0.99722
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