We propose a new family of univariate distributions generated from the Weibull random variable, called a new Weibull-X family of distributions. Two special sub-models of the proposed family are presented and the shapes of density and hazard functions are investigated. General expressions for some statistical properties are discussed. For the new family, three useful characterizations based on truncated moments are presented. Three different methods to estimate the model parameters are discussed. Monti Carlo simulation study is conducted to evaluate the performances of these estimators. Finally, the importance of the new family is illustrated empirically via two real life applications.

中文翻译：

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一个新的Weibull- X系列分布：特性，特征和应用

我们建议从Weibull随机变量生成一个新的单变量分布族，称为新的Weibull-X分布族。提出了所提出家族的两个特殊子模型，并研究了密度和危害函数的形状。讨论了一些统计属性的一般表达式。对于新家族，提出了基于截断矩的三个有用的表征。讨论了三种估计模型参数的方法。进行Monti Carlo模拟研究以评估这些估计量的性能。最后，通过两个现实生活中的经验来说明新家庭的重要性。