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The density of a mixture distribution with mixing distribution provides a way of finding nonparametric estimate of an unknown density.In this talk,given a set of count data,we are interested in estimating its underlying density.Estimating an unknown density by means of the mixture density involves the problem of estimating the unknown mixing distribution.We shall describe nonparametric estimation of the mixing distribution based on the power divergence family.Once the mixing distribution is estimated,a nonparametric estimate for probabilities of a count distribution can be straightaway obtained.