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On linear combination of generalized logistic random variables with an application to financial returns

Author

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  • Popović, Božidar V.
  • Mijanović, Andjela
  • Genç, Ali İ.

Abstract

We derive two expressions of the cumulative distribution function for the linear combination Z=αX+βY in case when X and Y are independent generalized logistic random variables. While the first expression is given in terms of infinite sums, the second expression is exact and it is given via the well known Fox H function. The exact cumulative distribution function of Z is derived by using Mellin and inverse Mellin transforms. We also consider two dependent logistic random variables case via Gumbel’s Type I bivariate logistic distribution and derive probability density function of the linear combination. The derived density function is found in elementary mathematical functions. In order to provide percentage points, we develop the numerical routine for calculation of the values of Fox H function. We study the application of the considered linear combination in the field of financial returns.

Suggested Citation

  • Popović, Božidar V. & Mijanović, Andjela & Genç, Ali İ., 2020. "On linear combination of generalized logistic random variables with an application to financial returns," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    • Handle: RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302800
    DOI: 10.1016/j.amc.2020.125314
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    References listed on IDEAS

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    1. del Castillo, J.M., 2016. "Slash distributions of the sum of independent logistic random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 111-118.
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    3. Laeven, Roger J.A. & Goovaerts, Marc J. & Hoedemakers, Tom, 2005. "Some asymptotic results for sums of dependent random variables, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 154-172, October.
    4. S. Satterthwaite & T. Hutchinson, 1978. "A generalisation of Gumbel's bivariate logistic distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 25(1), pages 163-170, December.
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