Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

Topic: Mode of InverseChiSquareDistribution
Replies: 1   Last Post: Nov 14, 2012 1:50 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
paulvonhippel at yahoo

Posts: 72
Registered: 7/13/05
Mode of InverseChiSquareDistribution
Posted: Nov 13, 2012 12:12 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2016. All Rights Reserved.