represents a distribution of the Pearson family with parameters , , , , and .
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.
Introduced in 2010