A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications
subject: estimation, extreme values, negative binomial distribution, mean residual life, discrete Lindley analog, COVID-19 data
description: 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.
creator: Ahmed Z. Afify, Abdulhakim A. Al-babtain, Abdul Hadi N. Ahmed
source: Entropy
publisher: MDPI AG
date: 2020
identifier: DOI: 10.3390/e22060603
coverage: Science, Astrophysics, Physics