A note on Sum, Difference, Product and Ratio of Kumaraswamy Random Variables

Abstract

Explicit expressions for the densities of S = X1 + X2 , D = X1 − X2 , P = X1X2 and R = X1/X2 are derived when X1 and X2 are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are mentioned in which such quantities might be of interest.

Keywords

• Ratio of random variables
• product of random variables
• Kumaraswamy distribution
• sub-independence