PolyaAeppliDistribution[, p]
represents a Polya-Aeppli distribution with shape parameters and p.


  • The Polya-Aeppli distribution is a compound geometric Poisson distribution, i.e. the distribution of a sum of independent identically distributed geometric random variates where the number of variates follows Poisson distribution.
  • The probability for positive integer value in a Polya-Aeppli distribution is proportional to p^(x-1) TemplateBox[{{1, -, x}, 2, {-, {{(, {{(, {1, -, p}, )},  , theta}, )}, /, p}}}, Hypergeometric1F1].
  • PolyaAeppliDistribution allows to be any positive real number, and p is a number between 0 and 1.
  • PolyaAeppliDistribution can be used with such functions as Mean, CDF, and RandomVariate.
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