Distributions of Sum, Difference, Product and Quotient of Independent Non-central Beta Type 3 Variables
Daya K. Nagar, Yeison Arley Ramirez-Vanegas
Journal of Advances in Mathematics and Computer Science · pp. 12–23 · Published 9 Mar 2013
10.9734/BJMCS/2013/1895Abstract
Let X and Y be independent random variables, X having a gamma distribution with shape parameter a and Y having a non-central gamma distribution with shape and non-centrality parameters b and δ , respectively. Define Z = X ⁄ (X+ 2Y ). Then, the random variable Z has a non-central beta type 3 distribution, Z ∼ NCB3(a, b; δ). In this article we derive density functions of sum, difference, product and quotient of two independent random variables each having noncentral beta type 3 distribution. These density functions are expressed in series involving first hypergeometric function of Appell.
Cited by 6
D. K. Nagar, Edwin Zarrazola, Yohana Tabares-Herrera · 2021
Avishek Mallick, I. Ghosh, G. Hamedani · Journal of Statistical Theory and Applications (JSTA) · 2018
C. C. Thiel, Theodore C. Zsutty · 2017
D. K. Nagar, A. Roldán-Correa · 2013
Wangyang Yu, W. Kleijn · IEEE/ACM Transactions on Audio Speech and Language Processing · 2021
Avishek Mallick, Carolina Wilmington, G. Hamedani
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