PearsonDistribution[a1, a0, b2, b1, b0]
represents a distribution of the Pearson family with parameters , , , , and .
PearsonDistribution[type, a1, a0, b2, b1, b0]
represents a Pearson distribution of given type.
- The probability density satisfies the differential equation .
- The Pearson family of distribution is historically divided into seven types. By giving the form PearsonDistribution[type, ...], the type will implicitly provide domain and parameter constraints.
- PearsonDistribution[1, ...] is a shifted and rescaled BetaDistribution.
- PearsonDistribution[2, ...] is a symmetric shifted and rescaled BetaDistribution.
- PearsonDistribution[3, ...] includes NormalDistribution and GammaDistribution.
- PearsonDistribution[4, ...] is not related to standard distributions.
- PearsonDistribution[5, ...] is a shifted InverseGammaDistribution.
- PearsonDistribution[6, ...] is a shifted and rescaled FRatioDistribution.
- PearsonDistribution[7, ...] is a shifted and rescaled StudentTDistribution.
- With symbolic parameters and no type argument, the first type whose parameter assumptions are not explicitly violated is assumed. Types are tried in the order: 4, 1, 6, 3, 5, 2, and 7.
- The parameter assumptions can be obtained from DistributionParameterAssumptions.
- PearsonDistribution can be used with such functions as Mean, CDF, and RandomVariate.
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