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A general stochastic model for bivariate episodes driven by a gamma sequence

Author

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  • Charles K. Amponsah

    (University of Nevada)

  • Tomasz J. Kozubowski

    (University of Nevada)

  • Anna K. Panorska

    (University of Nevada)

Abstract

We propose a new stochastic model describing the joint distribution of (X,N), where N is a counting variable while X is the sum of N independent gamma random variables. We present the main properties of this general model, which include marginal and conditional distributions, integral transforms, moments and parameter estimation. We also discuss in more detail a special case where N has a heavy tailed discrete Pareto distribution. An example from finance illustrates the modeling potential of this new mixed bivariate distribution.

Suggested Citation

  • Charles K. Amponsah & Tomasz J. Kozubowski & Anna K. Panorska, 2021. "A general stochastic model for bivariate episodes driven by a gamma sequence," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-31, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00120-5
    DOI: 10.1186/s40488-021-00120-5
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    References listed on IDEAS

    as
    1. Kozubowski, Tomasz J. & Panorska, Anna K. & Podgórski, Krzysztof, 2008. "A bivariate Lévy process with negative binomial and gamma marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1418-1437, August.
    2. Robert, Christian Y. & Segers, Johan, 2008. "Tails of random sums of a heavy-tailed number of light-tailed terms," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 85-92, August.
    3. Barreto-Souza, Wagner, 2012. "Bivariate gamma-geometric law and its induced Lévy process," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 130-145.
    4. 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.
    5. 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.
    6. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
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    Cited by:

    1. Kwame Boamah‐Addo & Tomasz J. Kozubowski & Anna K. Panorska, 2023. "A discrete truncated Zipf distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 156-187, May.

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