Linear Combination and Reliability of Generalized Logistic Random Variables

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3444

Keywords:

Generalized Logistic Distribution, Mellin Transform, Fourier Transform, H-function, Reliability

Abstract

Experimental random data, in general, present a skewed behaviour. Thus, asymmetrical generalized distributions are of interest. The generalized logistic distributions (GLDs) are good candidates to model skewed data because their probability density functions (p.d.f.) and characteristic functions are mathematically simple. In this paper, exact expressions in terms of the H-function are, for the first time, derived for the p.d.f. and for the cummulative distribution function of the linear combination of GLDs of type IV with different location, scale and shape parameters. Also, exact and approximate expressions are derived for $R=P(X<Y)$. Numerical examples illustrate the correctness of the expressions derived.

Author Biographies

Luan Carlos de Sena Monteiro Ozelim, University of Brasilia

Pushpa Narayan Rathie, University of Brasilia

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How to Cite

Ozelim, L. C. de S. M., & Rathie, P. N. (2019). Linear Combination and Reliability of Generalized Logistic Random Variables. European Journal of Pure and Applied Mathematics, 12(3), 722–733. https://doi.org/10.29020/nybg.ejpam.v12i3.3444