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InverseGammaDistribution

represents an inverse gamma distribution.

$ wo 'InverseGammaDistribution[2, 3]'
InverseGammaDistribution[2, 3]

Mean and variance are finite only for shape parameter α strictly greater than 1 and 2 respectively; the Piecewise default is Indeterminate:

$ wo 'Mean[InverseGammaDistribution[a, b]]'
Piecewise[{{b/(-1 + a), a > 1}}, Indeterminate]

$ wo 'Mean[InverseGammaDistribution[3, 2]]'
1

The median routes through InverseGammaRegularized:

$ wo 'Median[InverseGammaDistribution[a, b]]'
b/InverseGammaRegularized[a, 1/2]