Identifying the distribution of linear combinations of gamma random variables via Stein’s method

Dawei Lu and Jingcai Yang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 7, 2116-2123

Abstract: In Holm and Alouini (2004), an explicit formula for the probability density function of λ1−1Zr+λ2−1Z˜r was obtained, where λ1≠λ2≠0,Zr,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.

Date: 2023
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DOI: 10.1080/03610926.2021.1945104

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