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Abstract
The inverse Weibull distribution is one of the widely applied distribution for problems in reliability theory. In this article, we introduce a generalization—referred to as the Beta Inverse-Weibull distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of the Beta Inverse-Weibull distribution. The shapes of the corresponding probability density function and the hazard rate function have been obtained and graphical illustrations have been given. The distribution is found to be unimodal. Results for the non central moments are obtained. The relationship between the parameters and the mean, variance, skewness, and kurtosis are provided. The method of maximum likelihood is proposed for estimating the model parameters. We hope that this generalization will attract wider applicability to the problems in reliability theory and mechanical engineering.
Mathematics Subject Classification:
Acknowledgments
The authors are grateful to the referees for their constructive comments and valuable suggestions which certainly improved the presentation and quality of the article. This article was completed while Dr. B. M. Golam Kibria was on sabbatical leave (2010–2011). He is grateful to Florida International University for awarding him the sabbatical leave which gave him excellent research facilities.