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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
    1. Zeileis, Achim & Kleiber, Christian & Jackman, Simon, 2008. "Regression Models for Count Data in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i08).
    2. Mullahy, John, 1997. "Heterogeneity, Excess Zeros, and the Structure of Count Data Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 337-350, May-June.
    3. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    4. Barreto-Souza, Wagner, 2012. "Bivariate gamma-geometric law and its induced Lévy process," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 130-145.
    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.
    6. Biondi, Franco & Kozubowski, Tomasz J. & Panorska, Anna K. & Saito, Laurel, 2008. "A new stochastic model of episode peak and duration for eco-hydro-climatic applications," Ecological Modelling, Elsevier, vol. 211(3), pages 383-395.
    7. Muhammed Fatih Tüzen & Semra Erbaş, 2018. "A comparison of count data models with an application to daily cigarette consumption of young persons," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(23), pages 5825-5844, December.
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