Weighted Negative Binomial-Poisson Lindley with Application to Genetic Data

  • Hossein Zamani Department of Mathematics and Statistics, Faculty of Science, University of Hormozgan, Bandarabbas, Iran http://orcid.org/0000-0003-1126-6288
  • 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
Keywords: Weighted distribution, Poisson distribution, Discrete distribution, mixed distribution, Mixed Poisson


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.


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How to Cite
Zamani H, Ismail N, Shekari M. Weighted Negative Binomial-Poisson Lindley with Application to Genetic Data. jbe. 4(3):18-3.
Original Article(s)