This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# HotellingTSquareDistribution

 HotellingTSquareDistribution represents Hotelling's distribution with dimensionality parameter p and m degrees of freedom.
• The probability density for value in Hotelling's T-square distribution is proportional to for .
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (7)
Generate a set of pseudorandom numbers that are Hotelling's T-square 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:
The limiting value:
Kurtosis:
The limiting value:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
Hotelling's -statistic is used to test whether multivariate data has a given mean:
For multivariate normal data of length with mean , the test statistic follows a HotellingTSquareDistribution where is the dimension of the data:
Obtain the test statistic and -value for some data:
Alternatively, use TTest:
Parameter influence on the CDF for each :
Relationships to other distributions:
Hotelling's T-square distribution is a special case of FRatioDistribution:
Hotelling's T-square distribution is a special case of type 6 PearsonDistribution:
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