Certain Family of Weighted Averages with Beta Random Weights

A new specification for weighted averages of two independent and continuous random variables X1 and X2 with beta random weights is provided. Furthermore, it can be concluded that the randomly weighted averages with beta random proportions which is defined by Homei [H. Homei, Randomly weighted averages with beta random proportions 82, 15151520 (2012)] is a special case of the achievements of Soltani and Roozegar[A.R. Soltani, R. Roozegar, On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach 82, 10121020 (2012)]. A family including several specific examples is provided.

Randomly weighted average, Stieltjes transform, generalized Stieltjes transform, beta distribution