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Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede
Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
We investigate the length-biased inverse Weibull (LBIW) distribution, deriving its density function, hazard and reverse hazard functions, and reliability function. The moments, moment-generating function, Fisher information and Shannon entropy are also given. We discuss parameter estimation via the method of moments and maximum likelihood, and hypothesis testing for the LBIW and parent distributions.
Inequalities And Exponential Approximations For Residual Life Reliability Functions, Broderick O. Oluyede, Marvis Pararai
Inequalities And Exponential Approximations For Residual Life Reliability Functions, Broderick O. Oluyede, Marvis Pararai
Department of Mathematical Sciences Faculty Publications
Given that a unit is of age t, the remaining life after time t is random. The expected value of this random residual life is called the mean residual life at time t. Specifically, if T is the life of a component with distribution function F, then δF (t) = E(T −t|T > t) is called the mean residual life function (MRLF). It is well known that the class of distributions with decreasing mean residual life (DMR) contains the class of distributions with increasing hazard rate (IHR). In this note, …