Abstract
In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.
Highlights
The discrete probability distributions have their great importance in modeling real count data in many applied sciences such as public health, medicine, agriculture, epidemiology, and sociology, among others
We briefly study several estimators called, maximum likelihood estimator (MLE), maximum product of spacings estimator (MPSE), least-squares estimator (LSE), percentile estimator (PCE), Anderson-Darling estimator (ADE), Cramer-von-Mises estimator (CVME), weighted least-squares estimator (WLSE), and right-tail Anderson-Darling estimator (RADE)
We propose and study a new discrete distribution which has a log-concave probability mass function and an increasing discrete hazard rate function, for all choices of its parameter
Summary
The discrete probability distributions have their great importance in modeling real count data in many applied sciences such as public health, medicine, agriculture, epidemiology, and sociology, among others. Several discrete distributions have been introduced for modeling count data. Some traditional discrete models such as Poisson geometric distributions have limited applications in reliability, failure times, and counts. This is so, because some real count data show either under-dispersion or over-dispersion. This has motivated several statisticians to explore new discrete models based on classical continuous distributions for modeling discrete failure times and reliability data. There is still a clear need to construct more flexible discrete distributions to serve several applied areas such as social sciences, economics, and reliability studies to properly suit different types of count data. Al-Babtain et al (2020) proposed the natural discrete Lindley distribution. Eliwa et al (2020a, 2020c) proposed
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Pakistan Journal of Statistics and Operation Research
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
