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The generalized inverse Weibull distribution. (English) Zbl 1230.62014
Summary: The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the \(r\) th generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling life time data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing
62J20 Diagnostics, and linear inference and regression
62F10 Point estimation
62G30 Order statistics; empirical distribution functions
62H12 Estimation in multivariate analysis
65C60 Computational problems in statistics (MSC2010)
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