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Mode of InverseChiSquareDistribution

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  • Subject: [mg128642] Mode of InverseChiSquareDistribution
  • From: paul <paulvonhippel at>
  • Date: Tue, 13 Nov 2012 00:02:58 -0500 (EST)
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As a first step toward solving a more complicated problem, I would like to calculate the mode of the InverseChiSquareDistribution with D-1 degrees of freedom. The answer is 1/(D+1) but I am having trouble getting that expression from Mathematica.

First I type
 PDF[InverseChiSquareDistribution[D - 1]]
And then I cut and paste the function into ArgMax, imposing appropriate constraints:
 modeInverseChiSquare = ArgMax[{(2^((1 - D)/2) (1/x)^(1 + 1/2 (-1 + D)) E^(-(1/(2 x))))/ Gamma[1/2 (-1 + D)], x > 0, D > 0, Element[D, Integers]}, x, Reals]

But all ArgMax does is echo the input. If I evaluate the mode at a particular value of D I get the right answer -- e.g., modeInverseChiSquare /. D -> 10 returns 1/11. But what I'd like Mathematica to do is tell me that the answer in general is 1/(D+1).

Suggestions most welcome.

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