MultivariateStatistics`
MultivariateStatistics`

QuadraticFormDistribution

QuadraticFormDistribution[{a,b,c},{μ,Σ}]

represents the distribution of a quadratic form z.a.z+b.z+c for multivariate normal z.

Details and Options

Examples

open allclose all

Basic Examples  (2)

The mean of a quadratic form distribution:

The variance of a quadratic form distribution:

Scope  (3)

Generate a set of pseudorandom numbers that follow a quadratic form distribution:

Possible Issues  (2)

PDF and CDF can only be evaluated using Series:

Series expansion must be about the lower support point for the distribution:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:

Wolfram Research (2007), QuadraticFormDistribution, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/QuadraticFormDistribution.html.

Text

Wolfram Research (2007), QuadraticFormDistribution, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/QuadraticFormDistribution.html.

CMS

Wolfram Language. 2007. "QuadraticFormDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/QuadraticFormDistribution.html.

APA

Wolfram Language. (2007). QuadraticFormDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/MultivariateStatistics/ref/QuadraticFormDistribution.html

BibTeX

@misc{reference.wolfram_2024_quadraticformdistribution, author="Wolfram Research", title="{QuadraticFormDistribution}", year="2007", howpublished="\url{https://reference.wolfram.com/language/MultivariateStatistics/ref/QuadraticFormDistribution.html}", note=[Accessed: 25-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_quadraticformdistribution, organization={Wolfram Research}, title={QuadraticFormDistribution}, year={2007}, url={https://reference.wolfram.com/language/MultivariateStatistics/ref/QuadraticFormDistribution.html}, note=[Accessed: 25-July-2024 ]}