On the linear combination of independent logistic random variables

  • Filipe J. Marques NOVA University of Lisbon (FCT NOVA) and Center for Mathematics and Applications (CMA), Portugal
DOI: https://doi.org/10.19139/soic.v6i3.578
Keywords: Algebra of random variables, Shifted Gamma distribution, Generalized Integer Gamma distribution, Generalized logistic distributions, Difference of Generalized Integer Gamma distributions, mixtures

Abstract

In this work the exact distribution of the linear combination of p independent logistic random variables is studied. It is shown that the exact distribution may be represented as a shifted infinite sum of independent random variables distributed as the difference of two independent Generalized Integer Gamma distributions. In addition, two near-exact approximations are developed for this distribution. Numerical studies are conducted to access the degree of precision and also the computational performance of these approximations. The developed methodology is used to derive near-exact approximations for the linear combination of independent generalized logistic random variables.

Author Biography

Filipe J. Marques, NOVA University of Lisbon (FCT NOVA) and Center for Mathematics and Applications (CMA), Portugal
Departamento de Matematica, Faculdade de Ci ´ encias e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

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Published
2018-08-19
How to Cite
Marques, F. J. (2018). On the linear combination of independent logistic random variables. Statistics, Optimization & Information Computing, 6(3), 383-397. https://doi.org/10.19139/soic.v6i3.578
Issue
Vol 6 No 3 (2018)
Section
Research Articles
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