Transformed Semicircular Exponentiated Weibull Distribution

Abstract

Abstract In this paper, a new transformed Semicircular Exponentiated Weibull ( SEW ) distribution of three parameters is constructed by applying the transformation of the inverse stereographic projection that maps a real line to the unit circle. The cumulative distribution function, probability density function, expanded probability density function, and reliability measures are presented. Furthermore, the most important statistical aspects of this new distribution, such as moments, trigonometric moments, characteristic function, simulated data, quantile function, reliability stress strength model, Shannon entropy, and relative entropy are obtained. The maximum likelihood estimation method is implemented to estimate the unknown three parameters. A simulation study is conducted to detect empirically the behaviors of the maximum likelihood estimates of the SEW parameters for different default values of the parameters and different samples size.