pantole

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These are questions asked by pantole

The F-distribution (also known as Snedecor's F distribution or the Fisher-Snedecor distribution) depends on two separate degrees of freedom, m and n. It is defined by (Eq. 2 in MathWorld):

In Maple notation:

 

> fdist:=(x,m,n)->GAMMA((m+n)/2)*(m/n)^(m/2)/GAMMA(m/2)/GAMMA(n/2)*x^(m/2-1)/(1+m*x/n)^((m+n)/2);

In order to calculate the percentage points of the F-distribution we need to find the area under the curve. For example, for known m, n the integral

 

defines the percentage of points under curve for x, since  

This can be done easily in Maple, if we wish to find, say, 95 % confidence level for m=4, n=3, we (could) do the following:

> Fstat:=proc(perc,m,n) fsolve(int(fdist(u,m,n),u=0..x)-perc,x=0..infinity); end proc:

 

> Fstat(0.95,4,3);

          9.117182253

 

Is there a Maple built-in function I can use to calculate these values in a more elegant form instead of defining fdist and Fstat?

Is there something similar for the evaluation of the percentage points of the t-Distribution? 

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