Numerical values of the third data set.

This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of estimation were presented to estimate the parameters for the proposed family, such as maximum likelihood, ordinary least square, weighted least square, Anderson Darling, right-tailed Anderson-Darling, Cramér-von Mises, and maximum product of spacing methods. A special sub-model with three parameters called extended Modi exponential distribution was derived along with different shapes of its density and hazard functions. Randomly generated data sets and different estimation methods were used to illustrate the behavior of parameters of the proposal sub-model. To illustrate the importance of the proposed family over the other well-known methods, applications to medicine and geology data sets were analyzed.

本文提出一种全新方法，通过向某寿命分布族引入额外参数以拓展该分布族，提升其建模灵活性。该拓展分布族被命名为扩展Modi-G分布族（extended Modi-G family of distributions）。本文推导了所提分布族的一般统计性质，并针对该分布族提出了多种参数估计方法，包括极大似然估计、普通最小二乘估计、加权最小二乘估计、安德森-达令检验（Anderson-Darling test）、右尾安德森-达令检验、克拉默-冯·米塞斯检验（Cramér-von Mises test）以及间距最大乘积估计法。本文还推导了一个含三个参数的特殊子模型——扩展Modi指数分布（extended Modi exponential distribution），并给出了其概率密度函数与失效率函数的多种形状特征。通过随机生成的数据集与多种估计方法，验证了所提子模型的参数估计表现。为验证所提分布族相较于其他经典方法的优越性，本文分别针对医学与地质学数据集开展了应用分析。