weighted negative binomialpoisson lindley with application to genetic data

Background & aim: mixed poisson and mixed negative binomial distributions have been considered as alternatives for fitting count data with over-dispersion. this study introduces a new discrete distribution which is a weighted version of poisson-lindley distribution. methods & materials: the weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. the p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial- poisson-lindley (wnbpl), are provided. the maximum likelihood method for parameters estimation is also presented. results: the wnbpl distribution is fitted to several datasets, related to genetics and compared with the poison distribution. the goodness of fit test shows that the wnbpl can be a useful tool for modeling genetics datasets. conclusion: this paper introduces a new weighted poisson-lindley distribution which is obtained using negative binomial weight function and can be used for fitting over-dispersed count data. the p.m.f., p.g.f. and simulation procedure are provided for the new weighted distribution, namely the weighted negative binomial-poisson lindley (wnbpl) to better inform parents from possible time of occurrence reflux and treatment strategies.