"Jacek Gomoluch" <[EMAIL PROTECTED]> wrote in message
news:<9uqkmv$954$[EMAIL PROTECTED]>...
> In a stochastic process the number of customers which are arriving at a
> server (during a time intervall) is desribed by a Poisson distribution:
>
> P(n)=exp(-v) * (v^n)/(n!)
>
> Each arriving customer has a task to be carried out of which the size (in
> units) is described by a lognormal distribution:
>
> f(u)= exp(-(ln u)^2 / (2*a^2)) / (u*a*SQRT(2*PI))
>
> Question: What is the total number of units (i.e. size of all tasks)
> requested during the time intervall ?
>
> I wonder how these distributions can be concatenated, and if there is a
> formula for this.
If the count variable and the size variable are independent,
calculation of the mean and variance of the total is straightforward.
This kind of problem arises a lot in the actuarial literature (a
process for the number of claims and a process for the claim size),
and the Poisson and the lognormal have been used in this context - it
might be worth your while to look there for results.
Glen
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
