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InverseChiSquareDistribution

InverseChiSquareDistribution[Nu]
represents an inverse chi^2 distribution with Nu degrees of freedom.
InverseChiSquareDistribution[Nu, Xi]
represents a scaled inverse chi^2 distribution with Nu degrees of freedom and scale Xi.
  • The inverse chi^2 distribution InverseChiSquareDistribution[Nu] is the distribution followed by the inverse of a chi^2-distributed random variable with Nu degrees of freedom.
  • The inverse chi^2 distribution is commonly used in normal models for Bayesian data analysis.
EXAMPLESCLOSE ALL
Basic Examples   (2)
The mean and variance of an inverse chi^2 distribution:
Probability density function:
The mean and variance of an inverse chi^2 distribution:
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Probability density function:
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Scope   (4)
Generate a set of pseudorandom numbers that are inverse chi^2 distributed:
Pseudorandom scaled inverse chi^2 distributed numbers:
Properties based on higher-order moments:
Third moment of an inverse chi^2 distribution:
The 0.75 quantile of a scaled inverse chi^2 distribution with nu=10 and xi=2:
Applications   (2)
Plot the cumulative distribution function of the random variable:
A contour plot as both x and Nu are varied:
Properties & Relations   (5)
The probability density function integrates to unity:
Moments can be obtained from the characteristic function:
The two forms are related by a change of variable:
InverseChiSquareDistribution and ChiSquareDistribution have an inverse relationship:
Possible Issues   (2)
InverseChiSquareDistribution is not defined when either Nu or Xi is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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