A new trivariate model for stochastic episodes

• Main Authors: Francesco Zuniga, Tomasz J. Kozubowski, Anna K. Panorska
• Format: Article
• Language: English
• Published: SpringerOpen 2021-02-01
• Series: Journal of Statistical Distributions and Applications
• Subjects: BEG model; BGGE distribution; BTLG distribution; Extremes; Financial data; Geometric distribution
• Online Access: https://doi.org/10.1186/s40488-021-00114-3

Abstract We study the joint distribution of stochastic events described by (X,Y,N), where N has a 1-inflated (or deflated) geometric distribution and X, Y are the sum and the maximum of N exponential 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.