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The problem of estimating the compounding distribution of a compound Poisson process from independent observations of the compound process has been analyzed by Tucker (1963). A maximum likelihood method is proposed. The existence, uniqueness and convergence of the resulting estimator are derived. One obtains practical solutions by means of a very simple algorithm which is briefly described. A numerical example is presented in the risk business framework.
Léopold Simar (Mon,) studied this question.