Vol. 18, No. 1, 1966

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ISSN: 0030-8730
The sum of two independent exponential-type random variables

Edward Martin Bolger

Vol. 18 (1966), No. 1, 31–35
Abstract

Let X1, X2 be nondegenerate, independent, exponential-type random variables (r.v.) with probability density functions, (p.d.f.) f1(x1;𝜃), f2(x2;𝜃), (not necessarily with respect to the same measure), where fi(xi;𝜃) = exp{xipi(𝜃) + qi(𝜃)} for 𝜃 (a,b) and pi(𝜃) is an analytic function of 𝜃 (for Re 𝜃 (a,b)) with pi(𝜃) never equal to zero on (a,b). If X1, X2 are neither both normal nor both Poisson type r.v.’s, then X1 + X2 is an exponential-type r.v. if and only if p1(𝜃) = p2(𝜃).

Mathematical Subject Classification
Primary: 62.10
Milestones
Received: 17 August 1964
Revised: 26 February 1965
Published: 1 July 1966
Authors
Edward Martin Bolger