In this manuscript, we have derived a new lifetime distribution named generalized Weibull–Lindley (GWL) distribution based on the T-X family of distribution specifically the generalized Weibull-X family of distribution. We derived and investigated the shapes of its probability density function (pdf), hazard rate function, and survival function. Some statistical properties such as quantile function, mode, median, order statistics, Shannon entropy, Galton skewness, and Moors kurtosis have been derived. Parameter estimation was done through maximum likelihood estimation (MLE) method. Monte Carlo simulation was conducted to check the performance of the parameter estimates. For the inference purpose, two real-life datasets were applied and generalized Weibull–Lindley (GWL) distribution appeared to be superior over its competitors including Lindley distribution, Akash distribution, new Weibull-F distribution, Weibull–Lindley (WL) distribution, and two-parameter Lindley (TPL) distribution.

中文翻译：

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寿命数据建模中的广义Weibull-Lindley（GWL）分布

在本手稿中，我们基于TX分布族，特别是广义Weibull- X，推导了一个新的寿命分布，称为广义Weibull-Lindley（GWL）分布家庭分布。我们推导并研究了其概率密度函数（pdf），危险率函数和生存函数的形状。得出了一些统计特性，例如分位数函数，众数，中位数，阶数统计，香农熵，高尔顿偏度和摩尔峰度。参数估计是通过最大似然估计（MLE）方法完成的。进行了蒙特卡洛模拟，以检查参数估计的性能。出于推理目的，应用了两个真实的数据集，广义的威布尔–琳德利（GWL）分布似乎优于竞争对手，包括Lindley分布，Akash分布，新的Weibull- F分布，威布尔–琳德利（WL）分布和两参数Lindley（TPL）分布。