Abstract

In this article, we propose a new power Garima-generated (PG-G) family of distributions. It depends on a power Garima random variable as a generator. Three special models of the PG-G family are displayed: the power Garima–Fréchet, power Garima–Weibull, and power Garima–Lindley distributions. Some properties, including the quantile function, survival and hazard rate functions, moments, skewness, kurtosis, and order statistics, are derived. The algorithm for generating a random number that follows the PG-G family is proposed. The maximum likelihood estimation is employed to obtain the parameter estimators of the PG-G family. The efficiency and importance of the newly generated family are examined through real data sets. Moreover, the example for generating a random number and estimating the parameters of some special model of the PG-G distribution family are proposed with R code to demonstrate how it can be applied in data analysis.

中文翻译：

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Power Garima生成的分布族：特性和应用

摘要

在本文中，我们提出了由Garima生成（PG-G）的新功率分布族。它取决于功率Garima随机变量作为生成器。展示了PG-G系列的三种特殊型号：功率Garima–Fréchet，功率Garima–Weibull和功率Garima–Lindley分布。得出了一些特性，包括分位数函数，生存率和危险率函数，力矩，偏度，峰度和阶次统计量。提出了遵循PG-G系列的随机数生成算法。采用最大似然估计来获得PG-G系列的参数估计器。通过实际数据集检查了新产生的家庭的效率和重要性。而且，