A new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

中文翻译：

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新类 Lindley 分布：属性和应用

本文介绍了一个新的广义类 Lindley 分布。这个新类称为 T-Lindley{Y} 分布类，它是通过使用均匀分布、指数分布、威布尔分布、对数逻辑分布、逻辑分布和柯西分布的分位数函数生成的。讨论了包括模态、矩和香农熵在内的统计性质。更详细地研究了三个新的广义 Lindley 分布。为了估计未知参数，使用了最大似然估计并进行了模拟研究。最后，使用四个不同的数据集说明了这个新提出的类在拟合寿命数据方面的有用性。在应用部分，介绍了 T-Lindley{Y} 类成员在单峰和双峰数据集建模方面的优势。