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- W2070978514 abstract "If, for every $p in ( {0,1} ),p$ times a geometric $( p )$ sum of independent identically distributed nonnegative random variables has the same distribution as the individual random variables, then the random variables are exponentially distributed. The phase “for every $p in ( {0,1} )$ ” can be weakenedsomewhat, and if first moments are assumed to exist, it can be replaced by “for some $p in ( {0,1} )$.” Related characterizations of the power function distribution and of the Poisson process are discussed, as are the effects of dropping the assumption of nonnegativity of the random variables." @default.
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- W2070978514 date "1973-03-01" @default.
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- W2070978514 title "Some Characterizations of the Exponential Distribution by Geometric Compounding" @default.
- W2070978514 doi "https://doi.org/10.1137/0124025" @default.
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