Products and Ratios of Two Gaussian Class Correlated Weibull Random Variables

Abstract. Starting from on a recently introduced Gaussian class bivariate Weibull stochastic model, the probability density and the cumulative distribution functions of the product (Z1 Z2) c and the ratio (Z1/Z2) c, when Z1 and Z2 are correlated Weibull random variables belonging to this class (c> 0), are derived in closed form. Moreover, using the inequality between arithmetic and geometric mean, a union upper bound for the distribution of the sum of two correlated Weibull variates Zc1 + Z c 2 is also presented. Special cases of our results are in agreement with previously published ones. The proposed analysis is useful in several scientific fields of engineering