Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution

Abstract

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

A New Type of Bivariate-Gamma Probability Function

“…The use of Generalized Gamma distribution has garnered commendable attention of many researchers in a wide spectrum of studies due to its flexibility, robustness and small magnitude of entropy. [1] (survival analysis of ovarian cancer patients), [2] (lifetimes of industrial devices, serological reversal time in children of HIV-contaminated mothers), [3] (strength of materials: breaking stress of carbon fibers, repair times for an airborne communication transceiver), [4] and [5] adopted alpha power transformed Xgamma for modelling strength of materials and environmental data, respectively, while [6] generalized conventional gamma function to study fatigue of aluminum coupons and tensile strength of carbon fibers. [7]- [8] extended generalised gamma to Xgamma and transmuted inverse Xgamma distributions with application to zoonatic disease caused by coronavirus etc.…”