Modified Inverse Weibull Distribution

Abstract

A generalized version of four parameter modified inverse weibull distribution (MIWD) is introduced in this paper. This distribution generalizes the following distributions: (1) Modified Inverse exponential distribution, (2) Modified Inverse Rayleigh distribution, (3) Inverse weibull distribution. We provide a comprehensive description of the mathematical properties of the modified inverse weibull distribution along with its reliability behaviour. We derive the moments, moment generating function and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. The inverse weibull distribution is the life time probability distribution which is used in the reliability engineering discipline. The inverse weibull distribution can be used to model a variety of failure characteristics such as infant mortality, useful life and wear-out periods. Reliability and failure data both from life testing and in service records which is often modeled by the life time distributions such as the inverse exponential, inverse Rayleigh, inverse Weibull distributions. In this research we have developed a new reliability model called modified inverse weibull distribution. This paper focuses on all the properties of this model and presents the graphical analysis of modified inverse weibull reliability models. This paper present the relationship between shape parameter and other properties such as non- reliability function, reliability function, instantaneous failure rate, cumulative instantaneous failure rate models. This life time distribution is capable of modeling of various shapes of aging and failure criteria.The proposed model can be used as an alternative to inverse generalized exponential, inverse generalized Rayleigh, inverse generalized weibull distributions. The cumulative distribution function (CDF) of the Inverse weibull distribution is denoted by