Re: Mode of InverseChiSquareDistribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg128651] Re: Mode of InverseChiSquareDistribution*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Wed, 14 Nov 2012 01:27:46 -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*References*: <20121113050258.8E2766992@smc.vnet.net>

D is a reserved word and cannot be used for a variable name. The mode is the value of x for which the derivative of the PDF is zero. dist = InverseChiSquareDistribution[d - 1]; mode = x /. Solve[ Simplify[ D[PDF[dist, x], x] == 0, x > 0], x][[1]] 1/(1 + d) Bob Hanlon On Tue, Nov 13, 2012 at 12:02 AM, paul <paulvonhippel at yahoo.com> wrote: > 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. > > > > >

**References**:**Mode of InverseChiSquareDistribution***From:*paul <paulvonhippel@yahoo.com>