Re: Inconsistent behaviour of StudentTDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg103207] Re: [mg103162] Inconsistent behaviour of StudentTDistribution
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Thu, 10 Sep 2009 07:23:17 -0400 (EDT)
- Reply-to: hanlonr at cox.net
It just needs some help
PDF[StudentTDistribution[f], x]
(f/(f + x^2))^((f + 1)/2)/(Sqrt[f]*Beta[f/2, 1/2])
D[CDF[StudentTDistribution[f], x], x] /. Sign'[x] -> 0 //
FullSimplify[#, {Element[x, Reals], f > 0}] &
(f^(f/2)*(f + x^2)^(-(f/2) - 1/2))/Beta[f/2, 1/2]
% == %% // FullSimplify[#, {Element[x, Reals], f > 0}] &
True
Bob Hanlon
---- Alexey <lehin.p at gmail.com> wrote:
=============
Hello,
Consider the following:
PDF[StudentTDistribution[f], x]
D[CDF[StudentTDistribution[f], x], x]
The outputs of these expressions must be equal. But in really the
second is useless and confusing.