Bayesian analysis of three parameter singular Marshall-Olkin bivariate Pareto distribution

Marshall-Olkin exponential shock model covering all range of dependence

In this paper, we present a new Marshall-Olkin exponential shock model. The new construction method gives the proposed model further ability to allocate the common joint shock on each of the components, making it suitable for application in fields like reliability and credit risk. The given model has a singular part and supports both positive and negative dependence structure. Main dependence properties of the model is given and an analysis of stress-strength is presented. After a performance analysis on the estimator of parameters, a real data is studied. Finally, we give the multivariate ver…

双变量Beta分布：参数推断与诊断

Bivariate beta distribution: parameter inference and diagnostics

针对相关比例的概率建模难题，本文研究Olkin & Trikalinos（2015）提出的双变量Beta分布，给出频率学派与贝叶斯参数估计方法，讨论先验设定并开发模型诊断方法。

Bayesian Inference of a Dependent Competing Risk Data

Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks data set using four-parameter Marshall-Olkin bivariate Weibull distribution when the failure of an unit at a particular time point can happen due to more than one cause. The aim of this paper is to provide the Bayesian analysis of the same model based on a very flexible Gamma-Dirichlet prior on the scale parameters. It is observed that the Bayesian inferenc…

On Bivariate Exponentiated Extended Weibull Family of Distributions

In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains several bivariate lifetime models. Some mathematical properties of the new class of distributions are studied. We provide the joint and conditional density functions, the joint cumulative distribution function and the joint survival function. Special bivariate distributions are investigated in some detail. The maximum likelihood estimators are obtained using t…

On Bivariate Discrete Weibull Distribution

Recently, Lee and Cha (2015, `On two generalized classes of discrete bivariate distributions', {\it American Statistician}, 221 - 230) proposed two general classes of discrete bivariate distributions. They have discussed some general properties and some specific cases of their proposed distributions. In this paper we have considered one model, namely bivariate discrete Weibull distribution, which has not been considered in the literature yet. The proposed bivariate discrete Weibull distribution is a discrete analogue of the Marshall-Olkin bivariate Weibull distribution. We study various proper…

Univariate and Bivariate Geometric Discrete Generalized Exponential Distributions

Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have demonstrated their method for the exponential and Weibull classes. In the same paper they have briefly indicated regarding its bivariate extension. The main aim of this paper is to introduce the same method, for the first time, to the class of discrete generalized exponential distributions both for the univariate and bivariate cases. We investigate several properti…

A new semi-parametric family of probability distributions for survival analysis

In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it is possible to add more than a single parameter to a given distribution. We then introduce very flexible families of distributions for which we calculate some moments. Notably, we give some tractable expressions of these moments when the given baseline distribution is Log-logistic. Finally, we demonstrate how to generate sample from these new families.

Majorization: Here, There and Everywhere

The appearance of Marshall and Olkin's 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and Schur convexity in a broad spectrum of fields. After 25 years this continues to be the case. The present article presents a sampling of the diverse areas in which majorization has been found to be useful in the past 25 years.