A new trivariate model for stochastic episodes

We study the joint distribution of stochastic events described by (X,Y,N), whereNhas a 1-inflated (or deflated) geometric distribution andX,Yare the sum and the maximum ofNexponential random variables. Models with similar structure have been used in several areas of applications, including actuarial science, finance, and weather and climate, where such events naturally arise. We provide basic properties of this class of multivariate distributions of mixed type, and discuss their applications. Our results include marginal and conditional distributions, joint integral transforms, moments and related parameters, stochastic representations, estimation and testing. An example from finance illustrates the modeling potential of this new model.