Weighted negative binomial-Poisson Lindley with application to genetic data

• Main Authors: Hossein Zamani, Noriszura Ismail, Marzieh Shekari
• Format: Article
• Language: English
• Published: Tehran University of Medical Sciences 2018-12-01
• Series: Journal of Biostatistics and Epidemiology
• Subjects: Weighted distribution; Poisson distribution; Discrete distribution; mixed distribution; Mixed Poisson
• Online Access: https://jbe.tums.ac.ir/index.php/jbe/article/view/201

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.