On characterizations of exponential and gamma distributions

M. H. Alamatsaz

Statistics & Probability Letters, 1993, vol. 17, issue 4, 315-319

Abstract: As an interpretation of a general characterization concerning [alpha]-unimodal distributions due to Alamatsaz, the solution of the equation of recent interest is found where M and K (M > K) are integers, [alpha] > 0, U is uniformly distributed on (0, 1), Zi's are identical, Z1,...,ZK are independent and U, ZK+1,...,ZK+M are also independent. This yields several characterizations of exponential and gamma distributions and contains previous results of Kotz and Steutel (1988), Huang and Chen (1989), Yeo and Milne (1991) and Devroye (1990) in this connection. Then, a multivariate extension is discussed.

Keywords: Characterization; characteristic; function; [alpha]-unimodality; gamma; distribution; unimodality (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (4)

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