Marshall–Olkin bivariateWeibull distributions and processes

摘要

In this paper we introduce a new probability model known as type 2Marshall–Olkin bivariate Weibull distribution as an extension of type 1 Marshall- Olkin bivariate Weibull distribution of Marshall–Olkin (J Am Stat Assoc 62:30–44, 1967).Various properties of the newdistribution are considered. Bivariateminification processes with the two types ofWeibull distributions as marginals are constructed andtheir properties are considered. It is shown that the processes are strictly stationary. The unknown parameters of the type 1 process are estimated and their properties are discussed. Some numerical results of the estimates are also given.