Kamil Toth wrote:
> I have a simple question. Suppose I have a sequence of integers
> k[i],i=1,...,N drawn from the Poisson distribution. What is the
> distribution of random values x[i]=A*k[i], where A is a constant? Any
> hints or references are greatly appreciated. Note, I am not asking
> how to find distribution empirically, I would like to know what is
> the analytical form of distribution.
Do not seek mystical enlightenment.
The ``analytical'' form of the distribution is just
P(X = Ak) = P(Y = k) (where Y ~ Poisson(lambda))
= exp(-lambda) * (lambda^k)/k!
or, if you insist:
P(X = x) = exp(-lambda) * (lambda^(x/A))/((x/A)!) .
That is *all* you can say, and all you need to say. I.e.
``That is all ye know on earth and all ye need to know.''
There is no magic.
cheers,
Rolf Turner
rolf@math.unb.ca
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