Randomly weighted average with Dirichlet component proportions

ABSTRACT

This article introduces a new average of n independent continuous random variables X₁, …, X_n weighted by Dirichlet random components. A relation between the Cauchy–Stieltjes transforms of the distribution functions of this weighted average and X₁, …, X_n is established. Several examples illustrate usefulness and applicability of the result.

KEYWORDS:

• Cauchy–Stieltjes transform
• Dirichlet and beta distributions
• Multivariate B-spline
• Randomly weighted average

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E10
• 46F12
• 65R10

Acknowlegments

The authors would like to thank the Editor-in-Chief, the Administrator and anonymous referees for careful reading and for their valuable comments which greatly improved the paper. The author thank to the Yazd University for supporting this research. I lovingly dedicate this paper to my daughter who is the meaning of life.