"How to" for WP34s Poisson distribution  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: "How to" for WP34s Poisson distribution (/thread199859.html) 
"How to" for WP34s Poisson distribution  Dominic Richens  10062011 Have a look at this: Users' Guide: Poisson distribution It took me a long time to figure out the Poisson solver, mainly because the format the parameters needed to be in was not what I was used to. I assume I've got it right, since the answer is the same as this Poisson calculator.
Comments?
Re: "How to" for WP34s Poisson distribution  Paulo MO  10062011 I did not loose any time over this (and maybe I should ;) ) but when the User's Guide your link is pointing to says that "Assuming call interarrival times follow the Poisson distribution,...", probably what is meant is "Assuming that the number of call arrivals follows a Poisson distribution,...". A Poisson interarrival time would be nonsensical. This will, BTW, imply that the interarrival time is exponentially distributed. Who cares, right? :)
Paulo
Re: "How to" for WP34s Poisson distribution  Dominic Richens  10062011 I care! Bring it on! yeah, it is nonesense  thanks for the correct wording.
Two other things possibly wrong with the example: Re: "How to" for WP34s Poisson distribution  Walter B  10072011 Please read the footnote on page 16 of THE MANUAL. May help ;)
Walter
Re: "How to" for WP34s Poisson distribution  Alexander Oestert  10072011 In the manual I just downloaded, there is no footnote on page 16.
Re: "How to" for WP34s Poisson distribution  Dominic Richens  10072011 Yes, read that, know that much already :) I'm expecting to specify the mean and have it tell me the probability of X (as the footnote on page 48 says). I don't understand the lambda = n * p0 part. What does sample size n have to do with a Poisson distribution? In my example I used 8000 as the sample size but that's bogus  the 200 was a projection (the amount of traffic I think I'm going to have if I add more users). I could have used anything that kept the value of J =< 1 such than 200 = J * K and I get the same answer.
It works like the footnote on pg 48 if I always put p0 = 1 in J and the mean in K. I think the Remark for Poisson should say "Alternatively, Poisson's lambda = n*p0, may be in K if J = 1. Edited: 7 Oct 2011, 6:56 a.m.
Re: "How to" for WP34s Poisson distribution  Alexander Oestert  10072011 Would someone be so kind and point me in the right direction: I really don't find a footnote on page 16 of the WP34s manual. Are you talking about some other manual? Edited: 7 Oct 2011, 7:22 a.m.
Re: "How to" for WP34s Poisson distribution  Dominic Richens  10072011 Could be page 13  whatever page "STATISTICAL DISTRIBUTIONS, PROBABILITIES ETC. " is on in your version. I think Marcus and I are both using the new 2.2 version, not the 2.1 version in the zip file:
https://sourceforge.net/projects/wp34s/files/doc/
Re: "How to" for WP34s Poisson distribution  Alexander Oestert  10072011 Thanks, it is page 13. I was already using the recommended version.
Re: "How to" for WP34s Poisson distribution  Paul Dale  10072011 I thought this might cause a bit of confusion eventually.
I wanted a single parameter lambda for the Poisson distribution.
Re: "How to" for WP34s Poisson distribution  Dieter  10072011 I assume Walter had some very convincing reasons for this. But at the moment I simply cannot see which. ;) I am a big fan of POLA and KISS. Using two parameters for the Poisson distribution sure is possible, but not what I would consider consistent with the mentioned policy of least astonishment. Please, let's do it the way most users would expect and as also stated on the Wolfram Mathworld website on this subject. Especially the part between equations (8) and (9): "Note that the sample size N has completely dropped out of the probability function, which has the same functional form for all values of nu" (resp. lambda, since nu or lambda = N*p). Finally: if really two values p0 and n are given, pressing [x] returns the usual single parameter lambda. On the other hand, splitting a given lambda into n and a 1 that has be be stored in a separate register is awkward and an additional effort for most users who expect the usual singleparameter Poisson distribution.
Dieter
Re: "How to" for WP34s Poisson distribution  Paulo MO  10072011 This lambda= n*p0 is probably a leftover of the binomial distribution. The thing is: when you have a bunch of n repeated experiments, each with p0 probability of success (aka Bernoulli trials), then the mean number of successes is of course, n*p0, and the probability of k successes is given by the binomial distribution. Hurra for Poisson (who would have been a medical doctor, if he had been an obedient son)
Best Re: "How to" for WP34s Poisson distribution  Paul Dale  10072011 Quote: I don't remember the reasons, long long past now. Set p = 1 and n becomes lambda which didn't seem such a hardship to provide both view points.
Re: "How to" for WP34s Poisson distribution  Dominic Richens  10072011 Okay  so that's how I'm documenting it in the Users' Guide. I think the comment in the Owner's Manual should be changed to say p0 = 1 the mean can be put in K.
Re: "How to" for WP34s Poisson distribution  Dieter  10082011 I think you wrote a very nice and convincing explanation why the Poisson distribution on the 34s should be changed to the usual singleparameter definition. ;) It's simply the way most users will expect this distribution to work, and you explained the mathematical background behind this.
Dieter
Re: "How to" for WP34s Poisson distribution  Paulo MO  10082011 I totally agree with you, Dieter. Single parameter is the way to go. In a Poisson process, if someone forces us to state what N and p0 are, the only mathematically consistent answer is: N=infinity, p0=0. Having to, for example, put p0=1 in the 34s to make the thing work, would be a source of constant and unbearable mental agony :)
But hey, if that is the price to have a 34s, it's a small price;
Paulo
Re: "How to" for WP34s Poisson distribution  Dieter  10092011 They may live even a bit longer after this oddity has been corrected  it will give peace to their minds. ;)
Dieter
Re: "How to" for WP34s Poisson distribution  Walter B  10092011 Exactly that's the way it is described on page 48 of the manual. The parameters used for the binomial distribution may remain unchanged in J and K for Poisson as well. Alternatively, you may use the canonical Poisson's parameter in J while you store 1 in K.
HTH Re: "How to" for WP34s Poisson distribution  Dominic Richens  10092011 But it's actually the other way around. The 1 goes into J and the mean goes into K because anything greater than 1.0 in J causes "Invalid Parameter".
Re: "How to" for WP34s Poisson distribution  Walter B  10092011 Bonsoir Dominic, Looks like there's a mismatch between documentation and firmware. We'll get that settled. Thanks for pointing that out. Walter Edit: Changed the manual. Not committed yet.
Edited: 9 Oct 2011, 6:52 p.m.
