The name Pólya distribution has more than one use. It is a name for the negative binomial distribution , including
its extension to a positive real
number shape parameter (Boost C++ Libraries).
The name is also used for the number of draws of one color in a Pólya urn after a fixed number of draws. With positive reinforcement, this finite-count
law is a beta binomial distribution
(Siegrist). These uses refer to different families of discrete
distributions .
See also Beta Binomial Distribution ,
Negative Binomial Distribution ,
Pólya Urn
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References Boost C++ Libraries. "Negative Binomial Distribution." Boost.Math Documentation. https://www.boost.org/doc/libs/latest/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html . Siegrist,
K. "Pólya's Urn Process." In Random: Probability, Mathematical
Statistics, Stochastic Processes. https://www.randomservices.org/random/urn/Polya.html . Referenced
on Wolfram|Alpha Pólya Distribution
Cite this as:
Weisstein, Eric W. "Pólya Distribution."
From MathWorld https://mathworld.wolfram.com/PolyaDistribution.html
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