Inverse poisson

10042015, 06:52 PM
Post: #1




Inverse poisson
Accuracy of calculation (inclined to go with the Prime)...
Inverse Poisson with mean of 1E9 on Prime 1,000,073,566 Casio 9860gii 1,000,011,502 (Casio can't calculate for mean of 5E8, Prime hangs) WP 34s. Way off! TI nSpire Mean of 1E9 out of domain for calculation Can anyone find an accurate value to use as a benchmark? 

10042015, 07:43 PM
(This post was last modified: 10042015 09:09 PM by Dieter.)
Post: #2




RE: Inverse poisson
(10042015 06:52 PM)lrdheat Wrote: Inverse Poisson with mean of 1E9 on Prime 1,000,073,566 Fine  but for which probability ?) I assume it must be something like 0.01 resp. 0.99. (10042015 06:52 PM)lrdheat Wrote: WP 34s. Way off! I agree the Poisson (and Binomial) functions, especially the quantile functions, should get an update. Pauli and I had a discussion on this some months ago. The current, not yet completely finished code I proposed back then returns for p=0.01 a quantile of 999.926.434,656. This result may be flawed by inaccuracies in the regularized Gamma function used internally, so beware. Edit: result is correct – see below. (10042015 06:52 PM)lrdheat Wrote: TI nSpire Mean of 1E9 out of domain for calculation The problem seems to be the Poisson mass function where e^{–µ} · µ^{x} has to be evaluated. For µ=1E9 the first factor evaluates to zero in most environments, but there is a workaround by working with logs. ;) ADDENDUM: I checked the 34s result (using my improved, but currently not implemented algorithm) with Wolfram Alpha. Et voilà: the double precision result for p=0.01 and µ=1E9 is exact in 32 out of 34 digits. Which is about as good as it gets without additional guard digits: x = 999926434.65620471615794098329370... You may check this yourself by entering Q(1+x, 1E9) at Wolfram Alpha where x is the quantile you look for, i.e. here 999926434.6562... N.B.: Q(a, x) is the regularized incomplete Gamma function, which can be seen as a continuous (real) extension of the Poisson CDF. For integer x the Poisson CDF(x, µ) equals Q(x+1, µ). If you want an integer quantile, round up the result to get 999926435. Dieter 

10052015, 01:05 AM
Post: #3




RE: Inverse poisson
Sorry about not including probability...Using average of 1E9, at p=.99, what is correct value for inverse poisson? I'm guessing the Prime is closer than the Casio 9860gii.
Your new implementation sounds like a winner! 

10052015, 06:11 AM
(This post was last modified: 10052015 09:44 PM by Dieter.)
Post: #4




RE: Inverse poisson
(10052015 01:05 AM)lrdheat Wrote: Sorry about not including probability...Using average of 1E9, at p=.99, what is correct value for inverse poisson? I'm guessing the Prime is closer than the Casio 9860gii. This depends on whether you look at the left hand or right hand sum, i.e. the probability P(x≤X) or P(x>X). ;) The results I posted refer to the former. For p=0.99 there is a problem with the 34s regularized Gamma function (which returns values > 1 – sounds like a bug). Despite this my program returns an integer result of 1000073565 < x < 1000073566. With a corrected Gamma function the program returns... x = 1000073565.814426761131158060038507 ...which, according to Wolfram Alpha, seems to be the correct 34digit value for the 99%quantile. So the Prime is correct. Dieter Edit: sorry, the originally posted result was off by one... #) 

10072015, 12:45 PM
(This post was last modified: 10072015 12:46 PM by Dieter.)
Post: #5




RE: Inverse poisson  
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