About: (a,b,0) class of distributions

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In probability theory, a member of the (a, b, 0) class of distributions is any distribution of a discrete random variable N whose values are nonnegative integers whose probability mass function satisfies the recurrence formula for some real numbers a and b, where . Only the Poisson, binomial and negative binomial distributions satisfy the full form of this relationship. These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF–QVF).

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rdfs:label	(a,b,0) class of distributions (en)
rdfs:comment	In probability theory, a member of the (a, b, 0) class of distributions is any distribution of a discrete random variable N whose values are nonnegative integers whose probability mass function satisfies the recurrence formula for some real numbers a and b, where . Only the Poisson, binomial and negative binomial distributions satisfy the full form of this relationship. These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF–QVF). (en)
dcterms:subject	Actuarial science Discrete distributions Systems of probability distributions
Wikipage page ID	14204502 (xsd:integer)
Wikipage revision ID	1093218454 (xsd:integer)
Link from a Wikipage to another Wikipage	Actuarial science Discrete distributions Systems of probability distributions Natural exponential family Slope Logarithmic distribution Actuarial science Probability theory Binomial distribution Poisson distribution Negative binomial distribution Estimator bias Uniform distribution (discrete) Discrete random variable Panjer recursion Probability generating function
sameAs	(a,b,0) class of distributions (a,b,0) class of distributions (a,b,0) class of distributions (a,b,0) class of distributions
dbp:wikiPageUsesTemplate	dbt:ProbDistributions dbt:Reflist dbt:Short_description
has abstract	In probability theory, a member of the (a, b, 0) class of distributions is any distribution of a discrete random variable N whose values are nonnegative integers whose probability mass function satisfies the recurrence formula for some real numbers a and b, where . Only the Poisson, binomial and negative binomial distributions satisfy the full form of this relationship. These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF–QVF). More general distributions can be defined by fixing some initial values of pj and applying the recursion to define subsequent values. This can be of use in fitting distributions to empirical data. However, some further well-known distributions are available if the recursion above need only hold for a restricted range of values of k: for example the logarithmic distribution and the discrete uniform distribution. The (a, b, 0) class of distributions has important applications in actuarial science in the context of loss models. (en)
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is Link from a Wikipage to another Wikipage of	(a,b,0) Class of Distributions Negative binomial distribution Catalog of articles in probability theory Poisson-type random measure Panjer recursion
is Wikipage redirect of	(a,b,0) Class of Distributions
is foaf:primaryTopic of	wikipedia-en:(a,b,0)_class_of_distributions

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