Built-in Mathematica Symbol

ChiSquareDistribution

ChiSquareDistribution[

]
represents a

distribution with

degrees of freedom.

MORE INFORMATION

The probability density for value x in a distribution is proportional to for , and is zero for . »

For integer , the distribution with degrees of freedom gives the distribution of sums of squares of values sampled from a normal distribution.

ChiSquareDistribution allows to be any positive real number.

ChiSquareDistribution can be used with such functions as Mean, CDF and RandomReal. »

EXAMPLES

CLOSE ALL

Basic Examples (2)

The mean and variance of a

distribution:

Probability density function:

The mean and variance of a

distribution:

Probability density function:

Scope (4)

Generate a set of pseudorandom numbers that are

distributed:

Properties based on higher-order moments:

Third moment of a

distribution:

The 0.75 quantile of a

distribution with

:

Applications (3)

Compute the p-value for a

test with n degrees of freedom:

Plot the cumulative distribution function of the random variable:

A contour plot as both x and

are varied:

Properties & Relations (5)

The probability density function integrates to unity:

Moments can be obtained from the characteristic function:

ChiSquareDistribution is a special case of GammaDistribution:

The square root of a

variable follows the ChiDistribution:

ChiSquareDistribution and InverseChiSquareDistribution have an inverse relationship:

Possible Issues (2)

ChiSquareDistribution is not defined when

is not a positive real number:

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