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Multivariate Statistics Package Symbol

QuadraticFormDistribution

QuadraticFormDistribution[{a, b, c}, {

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

To use QuadraticFormDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].

QuadraticFormDistribution is the distribution of z.a.z+b.z+c for real-valued p×p symmetric positive definite matrix a, length p vector b, scalar c, and p-dimensional multivariate normal vector z.

QuadraticFormDistribution can be used with such functions as Mean and RandomReal.

The mean of a quadratic form distribution:

The variance of a quadratic form distribution:

Needs["MultivariateStatistics`"]

The mean of a quadratic form distribution:

Needs["MultivariateStatistics`"]

The variance of a quadratic form distribution:

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

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: