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A New Extension of Weibull Distribution with Application to Lifetime Data

A New Extension of Weibull Distribution with Application to Lifetime Data The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization, called alpha-power transformed Weibull distribution that provides better fits than the Weibull distribution and some of its known generalizations. The distribution contains alpha-power transformed exponential and alpha-power transformed Rayleigh distributions as special cases. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress–strength reliability and order statistics are derived. The distribution is capable of modeling monotonically increasing, decreasing, constant, bathtub, upside-down bathtub and increasing–decreasing–increasing hazard rates. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Two data sets have been analyzed to show how the proposed models work in practice. Further, a bivariate extension based on Marshall–Olkin and copula concept of the proposed model are developed but the properties of the distribution not considered in detail in this paper that can be addressed in future research. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

A New Extension of Weibull Distribution with Application to Lifetime Data

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Business and Management; Business and Management, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Computing Methodologies
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-016-0094-8
Publisher site
See Article on Publisher Site

Abstract

The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization, called alpha-power transformed Weibull distribution that provides better fits than the Weibull distribution and some of its known generalizations. The distribution contains alpha-power transformed exponential and alpha-power transformed Rayleigh distributions as special cases. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress–strength reliability and order statistics are derived. The distribution is capable of modeling monotonically increasing, decreasing, constant, bathtub, upside-down bathtub and increasing–decreasing–increasing hazard rates. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Two data sets have been analyzed to show how the proposed models work in practice. Further, a bivariate extension based on Marshall–Olkin and copula concept of the proposed model are developed but the properties of the distribution not considered in detail in this paper that can be addressed in future research.

Journal

Annals of Data Science – Springer Journals

Published: Jan 7, 2017

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