Reliability Properties of the NDL Family of Discrete Distributions with Its Inference

The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In t...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2021-05, Vol.9 (10), p.1139
Main Authors: Almazah, Mohammed Mohammed Ahmed, Alnssyan, Badr, Ahmed, Abdul Hadi N., Afify, Ahmed Z.
Format: Article
Language:English
Subjects:
closure reliability properties
Convolution
discrete Lindley analog
estimation
Food science
Least squares
Maximum likelihood estimation
Parameter estimation
partial orders
percentiles
Random variables
Reliability
total positivity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In the present article, we further investigate new results of value in the areas of both theoretical and applied reliability. To be specific, several closure properties of the NDL are proved. Among the results, sufficient conditions that maintain the preservation properties under useful partial orderings, convolution, and random sum of random variables are introduced. Eight different methods of estimation, including the maximum likelihood, least squares, weighted least squares, Cramér–von Mises, the maximum product of spacing, Anderson–Darling, right-tail Anderson–Darling, and percentiles, have been used to estimate the parameter of interest. The performance of these estimators has been evaluated through extensive simulation. We have also demonstrated two applications of NDL in modeling real-life problems, including count data. It is worth noting that almost all the methods have resulted in very satisfactory estimates on both simulated and real-world data.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9101139