Characterization, Characteristics And Parameter Estimation On Block-Basu Type Multivariate Exponential Distributions

Many experts and scholars pay more attentions to the exponential distributions, because of the application in the industrial technology. The Blcok-Basu type exponential distribution is the typical abstract absolute continuous exponential distribution, it was widely applied to the fatal shock mod- el and the competing risks model.The main results of the thesis are as follow:In the first part, introduction was given.In the second part, the characterization of the Block-Basu type tri-variate exponential distributions is studied. The partition of density of the Block-Basu type tri-variate exponential distributions derives the characterization. Stress-strength models of the Block-Basu type tri-variate exponential distributions are discussed and corresponding simulations of the Block-Basu type tri-variate exponential distributions are given.In the third part, the characteristics of the Block-Basu type tri-variate exponential distribution are discussed. The expectations, moments, coefficient of correlations and coefficient of partail correlations of the Block-Basu type tri-variate exponential distribution are derived, and the equivalent conditions of independence and irrelevance are given.In the fourth part, the parameter estimations of the Block-Basu type tri-variate exponential distribution are studied. The moment estimation and maximum likelihood estimation are derived.In the fifth part, naturally, the properties of the Block-Basu type multivariate exponential distribution are derived. Characterization, characteristics and parameter estimation of the Block-Basu type multivariate exponential distributions are given.