Bounded M-O Extended Exponential Distribution with Applications
-
Indranil Ghosh
,
Sanku Dey
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.
Acknowledgements
We are grateful to anonymous referees as well as the Edition-in-Chief for making some constructive suggestions and comments on an earlier version of the manuscript which resulted in this much improved version.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Notes on Cumulative Entropy as a Risk Measure
- Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues
- Optimal Control of a Dispatchable Energy Source for Wind Energy Management
- Bounded M-O Extended Exponential Distribution with Applications
- On Some Characterizations of the Levy Distribution
Artikel in diesem Heft
- Frontmatter
- Notes on Cumulative Entropy as a Risk Measure
- Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues
- Optimal Control of a Dispatchable Energy Source for Wind Energy Management
- Bounded M-O Extended Exponential Distribution with Applications
- On Some Characterizations of the Levy Distribution
