In this article, we introduce and study a new three-parameter distribution, called the Weighted Power Zeghdoudi (WPZ) distribution, which is formed by merging the weighted family and the power Zeghdoudi distribution. The probability density function of the WPZ distribution can be unimodal, right-skewed, or declining, demonstrating its great flexibility. An in-depth examination of the statistical features of the suggested distribution is provided. The maximum likelihood estimation approach is developed to estimate the unknown parameters utilizing simple random sampling and ranked set sampling. A simulation study is conducted to evaluate the performance of the estimation technique. Using two real data sets related to radiation datasets to demonstrate the relevance and adaptability of the model that was suggested by comparing it to other well-known statistical distributions using several goodness-of-fit measures, including the Kolmogorov–Smirnov (KS) statistic, the Cramér–von Mises (CvM) statistic, and the Anderson–Darling (AD) statistic, along with their associated p -values, such as; modified Weibull, length biased weighted Weibull, Weibull, gamma, and power Zeghdoudi models.
Mahnashi et al. (Sat,) studied this question.