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

Abstract

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.

Statistical analysis of the inverse power Zeghdoudi model: Estimation, simulation and modeling to engineering and environmental data

“…One of them is the power transformation technique of the research variable, and the resultant distribution is more flexible due to the shape parameter [2]. Some of the proposed power distributions are the power Cauchy distribution [3], the power Lindley distribution (PLD) [4], the power Shanker distribution [5], the power half logistic distribution [6], the power Lomax distribution [7], the power Aradhana distribution [8], the power binomial exponential distribution [9], the power Rama distribution [11], the power transmuted inverse Rayleigh distribution [10], the power Burr X distribution [12], the power XLindley distribution (PXLD) [13], the power inverted Topp-Leone distribution [14], the power Darna distribution [15], power modified Kies distribution [16] and the power ZD (PZD) [17], among others.…”

“…Our interest in the present study with a novel extension of the ZD with extra shape parameter ω > 0. The PZD is produced based on the transformation = w Z Y 1 , where Y follows the ZD with CDF (1)(see [17]). From the mathematical viewpoint, the CDF and the PDF of the PZD, for z > 0, δ > 0 and ω > 0, are as below:…”

“…Reference [17] mentioned that the density behavior of the PZD takes different shapes, including asymmetric and semi-symmetric, according to the parameter's values.…”

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

“…In recent years, many authors used the power transformation technique to obtain statistical distributions that are more flexible due to the shape parameter. Several of the potential power distributions are as follows: the power Zeghdoudi distribution [26], power modified Kies distribution [27], power Darna distribution [28], power Burr X distribution [29], power transmuted inverse Rayleigh distribution [30], power Rama distribution [31], power binomial exponential distribution [32], power Aradhana distribution [33], power Lomax distribution [34], power half logistic distribution [35], power Shanker distribution [36], power Lindley distribution [37], and power Cauchy distribution [38], among others.…”