MMK for heterogeneous data: identifiability, estimation and application

Abstract

Heterogeneous real datasets need complex probabilistic structures for a correct modeling. On the other hand, several generalizations of the Kumaraswamy distribution have been developed in the past few decades in an attempt to obtain better data adjustments that are limited in the interval (0,1). In this paper, we propose a mixture model of Kumaraswamy distributions (MMK) as a probabilistic structure for heterogeneous datasets with support in (0,1) and as an important generalization of the Kumaraswamy distribution. We derive the moments, the moment-generating function and analyze the failure rate function. Also, we prove the identifiability of the class of all finite mixtures of Kumaraswamy distributions. Via the EM-algorithm, we find estimates of maximum likelihood for the parameters of the MMK. Finally, we test the performance of the estimates by Monte Carlo simulation and illustrate an application of the proposed model using a real dataset.