Abstract
In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.
Highlights
Modeling of count data is found in many fields such as public health, medicine, epidemiology, applied science, sociology, and agriculture
It was found that the traditional discrete distributions have limited applicability as models for reliability, failure times, counts, etc
This has led to the development of some discrete distributions based on popular continuous models for reliability, failure times, etc
Summary
Modeling of count data is found in many fields such as public health, medicine, epidemiology, applied science, sociology, and agriculture. It was found that the traditional discrete distributions (geometric, Poisson, etc.) have limited applicability as models for reliability, failure times, counts, etc This is so, since many real count data show either over-dispersion, in which the variance is greater than the mean or under-dispersion, in which the variance is smaller than the mean. Several authors have used this discretization method of a continuous distribution to generate a corresponding discrete analog Following this approach, the most recent discrete distributions are due to Stein and Dattero [10], Roy [11,12,13], Krishna and Pundir [6], Jazi et al [7] and Gómez-Déniz [8].
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