A Continuous Estimator of a Mixing Distribution

Consider a portfolio of insurance policies where the mean frequency of claims for each policy may vary. This heterogeneity in the portfolio may be modeled as a distribution function F(X) that mixes the mean frequency 1. Using the observed claim frequencies of this portfolio, we present a continuous semiparametric estimator of the mixing distribution F(X) that has some unbiased moments and converges uniformly. The estimator that we investigate is a mixture of gamma distributions whose parameters are calculated by considering the determinants of certain moment matrices.