MATH 376 -- Probability and Statistics 2

Student's   t -distribution

January 23, 2004

>    read "/home/fac/little/public_html/ProbStat/MaplePackage/MSP.map";

55888131110

The following gives the form of the   t -distribution  pdf  with nu   degrees of freedom:

>    TPDF(nu,y);

GAMMA(1/2*nu+1/2)/GAMMA(1/2*nu)/(nu*Pi)^(1/2)/((1+y^2/nu)^(1/2*nu+1/2))

>    TP:=plot([y->TPDF(1,y),y->TPDF(3,y),y->TPDF(7,y)],-4..4,color=red):

>    NP:=plot(y->NormalPDF(0,1,y),-4..4,color=blue):

>    with(plots):

>    display(TP,NP);

[Maple Plot]

We see that the  t- distribution  pdf  has a shape similar to that of the standard

normal  N(0,1),  but with more probability "mass" concentrated in the tails.

As the number of degrees of freedom   nu  -> infinity ,  though, the   t- distribution

pdf approaches a standard normal:

>    plot([y->TPDF(100,y),y->NormalPDF(0,1,y)],-4..4);

[Maple Plot]

>