Built-in Mathematica Symbol

ChiDistribution

ChiDistribution[

]
represents a

distribution with

degrees of freedom.

MORE INFORMATION

ChiDistribution[] represents the distribution for the square root of a random variable.

ChiDistribution allows to be any positive real number.

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

EXAMPLES

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Basic Examples (2)

The mean and variance of a

distribution are related to the Gamma function:

Probability density function:

The mean and variance of a

distribution are related to the Gamma function:

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 (2)

Plot the cumulative distribution function of the random variable:

A contour plot as both x and

are varied:

Properties & Relations (6)

The probability density function integrates to unity:

Moments can be obtained from the characteristic function:

The square of a

variable follows the ChiSquareDistribution:

The

distribution with

is equivalent to HalfNormalDistribution with

:

The

distribution with

is equivalent to RayleighDistribution with

:

The

distribution with

is equivalent to MaxwellDistribution with

:

Possible Issues (2)

ChiDistribution is not defined when

is a not a positive real number:

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