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A New Family of Lifetime Distributions: Theory, Application and Characterizations

A New Family of Lifetime Distributions: Theory, Application and Characterizations A new class of distributions with increasing, decreasing, bathtub-shaped and unimodal hazard rate forms called generalized quadratic hazard rate-power series distribution is proposed. The new distribution is obtained by compounding the generalized quadratic hazard rate and power series distributions. This class of distributions contains several important distributions appeared in the literature, such as generalized quadratic hazard rate-geometric, -Poisson, -logarithmic, -binomial and -negative binomial distributions as special cases. We provide comprehensive mathematical properties of the new distribution. We obtain closed-form expressions for the density function, cumulative distribution function, survival and hazard rate functions, moments, mean residual life, mean past lifetime, order statistics and moments of order statistics; certain characterizations of the proposed distribution are presented as well. The special distributions are studied in some details. The maximum likelihood method is used to estimate the unknown parameters. We propose to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. It is observed that the proposed EM algorithm can be implemented very easily in practice. One data set has been analyzed for illustrative purposes. It is observed that the proposed model and the EM algorithm work quite well in practice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

A New Family of Lifetime Distributions: Theory, Application and Characterizations

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Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Subject
Business and Management; Business and Management, general; Statistics for Business, Management, Economics, Finance, Insurance; Artificial Intelligence
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-019-00216-5
Publisher site
See Article on Publisher Site

Abstract

A new class of distributions with increasing, decreasing, bathtub-shaped and unimodal hazard rate forms called generalized quadratic hazard rate-power series distribution is proposed. The new distribution is obtained by compounding the generalized quadratic hazard rate and power series distributions. This class of distributions contains several important distributions appeared in the literature, such as generalized quadratic hazard rate-geometric, -Poisson, -logarithmic, -binomial and -negative binomial distributions as special cases. We provide comprehensive mathematical properties of the new distribution. We obtain closed-form expressions for the density function, cumulative distribution function, survival and hazard rate functions, moments, mean residual life, mean past lifetime, order statistics and moments of order statistics; certain characterizations of the proposed distribution are presented as well. The special distributions are studied in some details. The maximum likelihood method is used to estimate the unknown parameters. We propose to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. It is observed that the proposed EM algorithm can be implemented very easily in practice. One data set has been analyzed for illustrative purposes. It is observed that the proposed model and the EM algorithm work quite well in practice.

Journal

Annals of Data Science – Springer Journals

Published: Mar 19, 2020

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