  We consider predictions of the random number and the magnitude of each iid
component in a random sum based on its distributional structure, where only a
total value of the sum is available and where iid random components are
non-negative. The problem is motivated by prediction problems in a Poisson shot
noise process. In the context, although conditional moments are best possible
predictors under the mean square error, only a few special cases have been
investigated because of numerical difficulties. We replace the prediction
problem of the process with that of a random sum, which is more general, and
establish effective numerical procedures. The methods are based on conditional
technique together with the Panjer recursion and the Fourier transform. In view
of numerical experiments, procedures work reasonably. An application in the
compound mixed Poisson process is also suggested.
