Identifying the distribution of linear combinations of gamma random variables via Stein's method. Issue 7 (3rd April 2023) - Lu, Dawei; Yang, Jingcai
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.