Mode of InverseChiSquareDistribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg128642] Mode of InverseChiSquareDistribution*From*: paul <paulvonhippel at yahoo.com>*Date*: Tue, 13 Nov 2012 00:02:58 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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.

**Follow-Ups**:**Re: Mode of InverseChiSquareDistribution***From:*Bob Hanlon <hanlonr357@gmail.com>