Bounded M-O Extended Exponential Distribution with Applications

Ghosh Indranil (), Dey Sanku () and Kumar Devendra ()
Additional contact information
Ghosh Indranil: Department of Mathematics and Statistics, University of North Carolina Wilmington, Wilmington, USA
Dey Sanku: Department of Statistics, St. Anthony’s College, Shillong-793001, Meghalaya, India
Kumar Devendra: Department of Statistics, Central University of Haryana, Haryana, India

Stochastics and Quality Control, 2019, vol. 34, issue 1, 35-51

Abstract: In this paper a new probability density function with bounded domain is presented. This distribution arises from the Marshall–Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advantage of not including any additional parameter(s) or special function in its formulation. The new transformed model, called the unit-Marshall–Olkin extended exponential (UMOEE) distribution which exhibits decreasing, increasing and then bathtub shaped density while the hazard rate has increasing and bathtub shaped. Various properties of the distribution (including quantiles, ordinary moments, incomplete moments, conditional moments, moment generating function, conditional moment generating function, hazard rate function, mean residual lifetime, Rényi and δ-entropies, stress-strength reliability, order statistics and distributions of sums, difference, products and ratios) are derived. The method of maximum likelihood is used to estimate the model parameters. A simulation study is carried out to examine the bias, mean squared error and 95 asymptotic confidence intervals of the maximum likelihood estimators of the parameters. Finally, the potentiality of the model is studied using two real data sets. Further, a bivariate extension based on copula concept of the proposed model are developed and some properties of the distribution are derived. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.

Keywords: Marshall–Olkin Extended Exponential Distribution; Maximum Likelihood Estimators; Monte Carlo Simulation (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/eqc-2018-0028 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ecqcon:v:34:y:2019:i:1:p:35-51:n:3

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/eqc/html

DOI: 10.1515/eqc-2018-0028

Access Statistics for this article

Stochastics and Quality Control is currently edited by George P. Yanev

More articles in Stochastics and Quality Control from De Gruyter
Bibliographic data for series maintained by Peter Golla ().