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Mode of InverseChiSquareDistribution
Posted:
Nov 13, 2012 12:12 AM


As a first step toward solving a more complicated problem, I would like to calculate the mode of the InverseChiSquareDistribution with D1 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.



