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The Transmuted Muth Generated Class of Distributions with Applications
Symmetry ( IF 2.940 ) Pub Date : 2020-10-14 , DOI: 10.3390/sym12101677
Abdulhakim A. Al-Babtain , Ibrahim Elbatal , Christophe Chesneau , Farrukh Jamal

Recently, the Muth generated class of distributions has been shown to be useful for diverse statistical purposes. Here, we make some contributions to this class by first discussing new theoretical facts and then introducing a natural extension of it via the transmuted scheme. The extended class is described in detail, emphasizing the characteristics of its probability and reliability functions, as well as its moments. Among other things, we show that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry. The mathematical inference of the parameters is also discussed. Special attention is paid to the distribution of the new class using the log-logistic distribution as a parent. In an applied work, we evaluate the behavior of the corresponding model by using simulated and practical data. In particular, we employ it to fit two real-life data sets, one with environmental data and the other with survival data. Standard statistical criteria validate the importance of the proposed model.

中文翻译:

具有应用程序的变换 Muth 生成分布类

最近,Muth 生成的分布类已被证明可用于各种统计目的。在这里,我们首先讨论新的理论事实,然后通过转换方案引入它的自然扩展,从而为这门课做出了一些贡献。对扩展类进行了详细描述,强调了其概率和可靠性函数的特点,以及它的矩。除其他外,我们表明它可以扩展父母分布的均值和方差的可能值,同时保持对称性或创建各种类型的不对称性。还讨论了参数的数学推论。特别注意使用对数逻辑分布作为父类的新类的分布。在应用作品中,我们通过使用模拟和实际数据来评估相应模型的行为。特别是,我们使用它来拟合两个现实生活中的数据集,一个是环境数据,另一个是生存数据。标准统计标准验证了所提议模型的重要性。
更新日期:2020-10-14
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