Abstract

The aim of this paper is to consider the bivariate inverse generalized exponential distribution which has a singular component. The bivariate inverse generalized exponential distribution can be used when the marginals have heavy tailed distributions, and they have non-monotone hazard functions. Due to presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four dimensional optimization problem. To avoid that we have proposed to use an EM algorithm and it involves solving only one non-linear equation at each ‘E’-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the model.

摘要

本文的目的是考虑具有奇异分量的二元逆广义指数分布。当边缘具有重尾分布且具有非单调风险函数时，可以使用双变量逆广义指数分布。由于奇异成分的存在，当数据中存在联系时，它可以非常有效地使用。由于它有四个参数，它是一个非常灵活的双变量分布，可以非常有效地用于分析各种双变量数据集。已经获得了几个依赖属性和依赖度量。最大似然估计量不能以封闭形式获得，它涉及解决四维优化问题。为避免这种情况，我们建议使用 EM 算法，它涉及在每个“E”步仅求解一个非线性方程。因此，所提出的 EM 算法的实现在实践中非常直接。已经进行了广泛的模拟实验和一个数据集的分析。我们观察到双变量逆广义指数分布可用于对相关竞争风险数据进行建模。已分析一组数据以显示模型的有效性。我们观察到双变量逆广义指数分布可用于对相关竞争风险数据进行建模。已分析一组数据以显示模型的有效性。我们观察到双变量逆广义指数分布可用于对相关竞争风险数据进行建模。已分析一组数据以显示模型的有效性。