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A new trivariate model for stochastic episodes

Author

Listed:
  • Francesco Zuniga

    (University of Nevada)

  • Tomasz J. Kozubowski

    (University of Nevada)

  • Anna K. Panorska

    (University of Nevada)

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.

Suggested Citation

  • Francesco Zuniga & Tomasz J. Kozubowski & Anna K. Panorska, 2021. "A new trivariate model for stochastic episodes," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-21, December.
  • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00114-3
    DOI: 10.1186/s40488-021-00114-3
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    References listed on IDEAS

    as
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    5. Wagner Barreto‐Souza & Rodrigo B. Silva, 2019. "A bivariate infinitely divisible law for modeling the magnitude and duration of monotone periods of log‐returns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(2), pages 211-233, May.
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