Statistical Analysis Of Bivariate Exponential Distribution

Discrete bivariate exponential distribution, as a bivariate extension of exponential distribution, is displayed in this paper. The statistical analysis of step-stress accelerated life testing of MOBVE distribution has been given. Two new exponential distributions have been derivated with copulas. Firstly, the estimators of parameters of MOBVE distribution on TFR model and CE model under step-stress accelerated life testing have been discussed. For TFR model, the maximum likelihood estimators of parameters are discussed in two different cases, respectively. Besidely, the precisions of the above estimates are investigated by large numbers of Monte-Carlo simulations. For CE model, the maximum likelihood estimators of parameters and the numerical example have been given. Secondly, a new bivariate exponential distribution, which is named FGMBVE distribution has been derivated with Farlie-Gumbel-Morgenstern copula. The definition and generating theory of FGMBVE distribution have been gived. The main properties are discussed. The moment estimates and the maximum likelihood estimates of the parameters are given under the series system in two different cases, respectively. Finally, another new bivariate exponential distribution, which is named CABVE distribution has been derivated with Cuadras-Auge copula.The similar work has been completed on CABVE distribution.