A New Three-Parameter Weibull Inverse Rayleigh Distribution: Theoretical Development and Applications

In this work, a three-parameter Weibull Inverse Rayleigh (WIR) distribution is proposed. The new WIR an extension of one-parameter that incorporated transformation the and Log-logistic as quantile function. statistical properties such function, order statistic, monotone likelihood ratio property, hazard, reverse hazard functions, moments, skewness, kurtosis, linear representation proposed were studied theoretically. maximum estimators cannot be derived in explicit form. So we employed iterative procedure called Newton Raphson method to obtain estimators. Bayes for scale shape parameters under squared error, Linex, Entropy loss functions are provided. obtained explicitly. Hence adopted numerical approximation known Lindley's other Simulation procedures see effectiveness different applications demonstrated on three real-life data sets. Further results showed performed credibly well when compared with five related existing skewed distributions. It was observed Bayesian estimates performs better than classical method.