The Power Zeghdoudi Distribution: Properties, Estimation, and Applications to Real Right-Censored Data

A new two-parameter power Zeghdoudi distribution (PZD) is suggested as a modification of the Zeghdoudi distribution using the power transformation method. As a result, the PZD may have increasing, decreasing, and unimodal probability density function and decreasing mean residual life function. In addition, other properties are presented, such as moments, order statistics, reliability measures, Bonferroni and Lorenz curves, Gini index, stochastic ordering, mean and median deviations, and quantile function. Following this, a section is devoted to the related model parameters which are estimated using the maximum likelihood estimation method, the weighted least squares and least squares methods, the maximum product of spacing method, the Cramer–von Mises method, and the right-tail and left-tail Anderson–Darling methods, and the Nikulin–Rao–Robson test statistic is considered. A simulation study is conducted to assess these methods and to investigate the distribution properties with right-censored data. The applicability of the proposed model is studied based on three real data sets of failure times, bladder cancer patients, and glass fiber data with a comparison with such competitors as the gamma, xgamma, Lomax, Darna, power Darna, power Lindley, and exponentiated power Lindley models. According to several established criteria, the comparative findings are overwhelmingly favorable to the suggested model.