This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# ChiDistribution

 ChiDistribution[] represents a distribution with degrees of freedom.
Probability density function:
Cumulative distribution function:
Mean and variance of a distribution are related to the Gamma function:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance of a distribution are related to the Gamma function:
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Median:
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 Scope   (7)
Generate a set of pseudorandom numbers that are distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Skewness:
In the limit the distribution becomes symmetric:
Kurtosis:
In the limit the distribution has the same kurtosis as NormalDistribution:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
Components of a 4D vector are normally distributed. Find the distribution of the length of the vector:
Find the average length of the vector:
Simulate possible lengths for a sample of 30 vectors:
Parameter influence on the CDF for each :
ChiDistribution[] converges to a normal distribution as ->∞:
Relationships to other distributions:
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 :
distribution is a special case of GammaDistribution:
The norm of standard normally distributed variables is a distribution:
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:
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