We derive two expressions of the cumulative distribution function for the linear combi-nation Z = alpha X + beta Y 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 pro-vide 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. (C) 2020 Elsevier Inc. All rights reserved.