🚀 go-pugleaf

In article <1992Oct8.202310.10461@ultb.isc.rit.edu> jsvrc@rc.rit.edu (J A Stephen Viggiano) writes:
>In article <1992Oct7.025857.28031@news2.cis.umn.edu> lee@hecto.cs.umn.edu (YoungJun Lee) writes:
>>
>> The stat. book I have just says that
>>  "Binomial distribution with n trials and success probability p can be
>>   approximated by possion distribution(when n is large, p is very small, and
>>   np is of moderate magnitude" and normal distribution(when n is large and
>>   p is not too near 0 or 1)"
>
>For the Poisson approximation, it is much more important for p to be small
>than it is for n to be large. The approximation is quite acceptable for n = 1
>with p <= 0.01. This can be seen by looking at the relative error in the
>variance; it involves only p.
>

Strictly speaking, the approximation is based on the fact that the
a sequence of binomial random variables converges in distribution
to a Poisson if n --> inf and p --> 0 in such a way that np --> lambda.
So, it's not so much that it's important for p to be small as it is that
np be small relative to n.  In other words, the mass function has to be
stacked up near 0.

I ought to pay small extra today because I'm working it so hard.