WishartDistribution
WishartDistribution[Σ,m]
represents a Wishart distribution with scale matrix Σ and degrees of freedom parameter m.
更多信息和选项
- To use WishartDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
- The probability density for a symmetric positive definite matrix
in a Wishart distribution is proportional to 
. - The scale matrix Σ can be any symmetric positive definite matrix. The parameter m can be any number such that m>Length[Σ].
- For integer m, the Wishart distribution gives the distribution of covariance matrices of multinormal samples.
- WishartDistribution can be used with such functions as Mean, PDF, and RandomReal.
范例
打开所有单元 关闭所有单元基本范例 (3)
Needs["MultivariateStatistics`"]The mean of a Wishart distribution:
Mean[WishartDistribution[{{Subscript[σ, 11]^2, ρ * Subscript[σ, 11] * Subscript[σ, 22]}, {ρ * Subscript[σ, 11] * Subscript[σ, 22], Subscript[σ, 22]^2}}, 10]]Needs["MultivariateStatistics`"]Variance[WishartDistribution[{{Subscript[σ, 11]^2, ρ * Subscript[σ, 11] * Subscript[σ, 22]}, {ρ * Subscript[σ, 11] * Subscript[σ, 22], Subscript[σ, 22]^2}}, 10]]Needs["MultivariateStatistics`"]PDF[WishartDistribution[{{1, ρ}, {ρ, 1}}, 10], {{Subscript[x, 11], Subscript[x, 12]}, {Subscript[x, 12], Subscript[x, 22]}}]Scope (3)
Needs["MultivariateStatistics`"]Generate a set of pseudorandom matrices that follow a Wishart distribution:
RandomReal[WishartDistribution[{{1, 1 / 3}, {1 / 3, 1}}, 5], 5]Needs["MultivariateStatistics`"]Skewness[WishartDistribution[{{1, 1 / 3}, {1 / 3, 1}}, 5]]Needs["MultivariateStatistics`"]Kurtosis[WishartDistribution[{{1, 1 / 3}, {1 / 3, 1}}, 5]]Possible Issues (2)
Needs["MultivariateStatistics`"]WishartDistribution is not defined when Σ is not symmetric and positive definite:
Mean[WishartDistribution[{{1, 2}, {0, 1}}, 5]]
WishartDistribution is not defined when m<Length[Σ]:
Mean[WishartDistribution[{{1, 0}, {0, 1}}, 1]]Needs["MultivariateStatistics`"]Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
Mean[WishartDistribution[{{Subscript[s, 11], Subscript[s, 12]}, {Subscript[s, 12], Subscript[s, 22]}}, m]] /. {Subscript[s, 11] -> 1, Subscript[s, 22] -> 1, Subscript[s, 12] -> 0, m -> I}文本
Wolfram Research (2007)，WishartDistribution，Wolfram 语言函数，https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html.
CMS
Wolfram 语言. 2007. "WishartDistribution." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html.
APA
Wolfram 语言. (2007). WishartDistribution. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html 年