Inference on the parameters and reliability characteristics of the generalized inverse Weibull distribution based on records

Abstract

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three parameters generalized inverse Weibull distribution with decreasing and unimodal failure rate is studied. Two measures of reliability are discussed, namely R(t) = P(X > t) and P = P(X > Y). Point and interval estimation procedures are developed for the parameters, R(t) and P based on records. Two point estimators are developed, namely uniformly minimum variance unbiased estimators (UMVUE) and maximum likelihood estimators (MLE). A comparison of different methods of estimation is done through simulations and asymptotic confidence intervals of the parameters based on MLE and log transformed MLE are constructed. Confidence intervals for the MLE and UMVUE of the parametric functions are obtained. Testing procedures are also developed for various hypotheses.