Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Computer Science Applications,Statistics and Probability
Reference36 articles.
1. Alshkaki, R. S. A.: On zero-one inflated geometric distribution. Internat. Res. J. Math. Eng. IT. 3(8), 10–21 (2016).
2. Arendarczyk, M., Kozubowski, T. J., Panorska, A. K.: A bivariate distribution with Lomax and geometric margins. J. Korean Statist. Soc. 47, 405–422 (2018a).
3. Arendarczyk, M., Kozubowski, T. J., Panorska, A. K.: The joint distribution of the sum and the maximum of dependent Pareto risks. J. Multivar. Anal. 167, 136–156 (2018b).
4. Aryal, T.: Inflated geometric distribution to study the distribution of rural outmigrants. J. Instit. Eng. 8(1), 266–268 (2011).
5. Barreto-Souza, W.: Bivariate gamma-geometric law and its induced Lévy process. J. Multivar. Anal. 109, 130–145 (2012).