Identifying the distribution of linear combinations of gamma random variables via Stein's method. Issue 7 (3rd April 2023)

• Record Type: Journal Article
• Authors: Lu, Dawei; Yang, Jingcai
• Is Part Of: Communications in statistics. Volume 52:Issue 7(2023)
• Page Start: 2116
• Page End: 2123
• Publication Date: 2023-04-03
• Subjects: Gamma random variables -- probability density function -- Stein's method; 60E05 -- 62E15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1945104
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In Holm and Alouini (2004 ), an explicit formula for the probability density function of λ 1 − 1 Z r + λ 2 − 1 Z ˜ r was obtained, where λ 1 ≠ λ 2 ≠ 0, Z r, Z ˜ r are independent identical random variables with Γ ( r, 1 ) distribution. In this paper, we use a recent technique from Gaunt (2018 ) involving Stein's method literature to obtain some simple and new proofs, which could also be used in other problems as a general method.