Tehran University of Medical Sciences Journal of Biostatistics and Epidemiology 2383-4196 4 3 2018 12 05 136 141 EN Hossein Zamani Department of Mathematics and Statistics, Faculty of Science, University of Hormozgan, Bandarabbas, Iran Noriszura Ismail School of Mathematical Sciences, Universiti Kebangsaan Malaysia, Malaysia Marzieh Shekari Department of Mathematics and Statistics, Faculty of Science, University of Hormozgan, Bandarabbas, Iran 2018 06 09 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. https://jbe.tums.ac.ir/index.php/jbe/article/view/201 https://jbe.tums.ac.ir/index.php/jbe/article/download/201/169