Abstract
In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.
Highlights
The inverse Weibull (IW) distribution is an important probability distribution which can be used to analyze the life time data with some monotone failure rates
Plots of the hrf of the inverse Weibull Weibull (IWW), inverse Weibull Pareto (IWP), inverse Weibull uniform (IWU) and IWBXII models are described in Figure 2 for some selected parameter values
This section concerns with the maximum likelihood estimates (MLEs) of the unknown parameters for the new family based on complete samples
Summary
The inverse Weibull (IW) distribution is an important probability distribution which can be used to analyze the life time data with some monotone failure rates. Based on lower record values, Sultan (2008) derived the Bayesian estimators and obtained the estimators of the reliability and hazard functions for the unknown parameters of the inverse Weibull distribution. Hassan and Al-Thobety (2012) provided optimum simple failure step stress partially accelerated life tests for the model parameters and acceleration factor for inverse Weibull model. Hassan et al (2015) discussed the constant–stress partially accelerated life test for inverse Weibull model based on multiple censored data. We provide a new family of distributions using inverse Weibull as a generator with the hope that it will attract a wider application in some areas.
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