Two Characterizations for Pascal Signals in Additive Noise.
CALIFORNIA UNIV DAVIS DEPT OF MATHEMATICS
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Let X be a nonnegative interger-valued random variable whose distribution is the convolution of a Pascal distribution and another distribution on the nonnegative integers which does not depend on the Pascal parameters. The class of all such convolutions satisfying certain moment conditions is characterized by a system of differential equations satisfied by their probability mass functions. The result contains a characterization of Pascal distributions obtained by Boswell and Patil 1973 as a special case. A characterization of convoluted geometric distributions not requiring moment conditions is also given. Author
- Statistics and Probability