Several two-component mixture distributions for count data
Razik Ridzuan Mohd Tajuddin, Noriszura Ismail, Kamarulzaman Ibrahim · Communications in Statistics - Simulation and Computation · 2020
Finite mixture model is a flexible approach for modeling multimodal data. Multimodality can be present in the data when the data constitute several subpopulations. In this study, several two-component mixture distributions for count data are proposed and described to cater for bimodality issue. The distributions considered in developing mixture distributions are Poisson (P), Poisson Lindley (PL), negative binomial (NB) as well as negative binomial Lindley (NBL), and altogether, a total of ten two-component mixture distributions are obtained. The maximum likelihood estimators for each mixture distribution are obtained by employing the L-BFGS-B method. A comparison study based on graphical approach is conducted to investigate the effect of mixing proportion on the resulting mixture distribution which are found based on different shapes of probability curve and positions of the mode. A simulation study is conducted to investigate the performance of each mixture distribution in fitting data that come from two subpopulations with different mean and dispersion values. Three mixture models which are P-NB, PL-NB and NB-NB, are the most commonly identified as adequate in describing the simulated data with various different types of mixing properties. These three distributions are considered to be the most flexible and thus, suggested for real data applications.