Letac, Gérard A characterization of the gamma distribution. (English) Zbl 0579.60013 Adv. Appl. Probab. 17, 911-912 (1985). This note first establishes that if \(\alpha >0\), there exists a positive random variable (rv) Y such that (*) \(E(Y^ s)=(1+(s/\alpha))^{(\alpha +s)}\), for all \(s>0\). The main result shows that if X and Y are independent rvs and condition (*) holds, then XY exp(-X/\(\alpha)\) and X are identically distributed if, and only if, X is a gamma rv with parameter \(\alpha\). Reviewer: H.N.Nagaraja Cited in 1 ReviewCited in 3 Documents MSC: 60E05 Probability distributions: general theory 62E10 Characterization and structure theory of statistical distributions 60E10 Characteristic functions; other transforms Keywords:characterization; gamma distribution; stationary distribution PDFBibTeX XMLCite \textit{G. Letac}, Adv. Appl. Probab. 17, 911--912 (1985; Zbl 0579.60013) Full Text: DOI