Question:solve and fsolve woes wi

Question:solve and fsolve woes wi

Maple

In a previous thread here I was looking at working with a noncentral F distribution. I have since found out what I need to be doing is a bit different.

The theory is as follows:

So, The F(1-alpha, nu1,nu2) is actually a Quantile value of the central F distribution. In my case, I'm trying to find a minimum sample size where nu1=3 and nu2=3*n. I transform the Power Equation into a function of into a cumulative distribution question using the formula P(A>B)=1-P(A<=B).

My maple implentation is as follows:

restart:with(Statistics):with(plots):

X := RandomVariable(FRatio(nu, omega));Y:= RandomVariable(FRatio(nu2, omega));

nu:=3;nu2:=3+2*i;omega:=3.0*n; delta:=0.82;

#Finding the Quantile Value of F(1-alpha,3,3*n)

CDF(X,u);

solve(1/n^(1.5)*u^(1.5)*hypergeom([1.5, 1.5+1.5*n],[2.5],-1./n*u)/GAMMA(1.5*n)=0.95,u);

#substitute into the CDF of Y and using the formula from the theory.
S:=sum(0.82^i/(i!*exp(0.82))*CDF(Y,3/(3+2*i)*RootOf(20*hypergeom([3/2, 3/2+3/2*n],[5/2],-1/n*_Z^2)*_Z^3-19*n^(3/2)*GAMMA(3/2*n))^2),i=0..infinity)=0.1;
solve(S,n);
Error, (in solve) cannot solve expressions with limit(2*GAMMA(3/2+i+3/2*n)*(3333333333/10000000000*(3+2*i)/n)^(3/2+i)*Heaviside(_t)*_t^(3/2+i)*hypergeom([3/2+i, 3/2+i+3/2*n],[5/2+i],-3333333333/10000000000*(3+2*i)*_t/n)/GAMMA(3/2+i)/GAMMA(3/2*n)/(3+2*i),_t = 3/(3+2*i)*RootOf(20*hypergeom([3/2, 3/2+3/2*n],[5/2],-1/n*_Z^2)*_Z^3-19*n^(3/2)*GAMMA(3/2*n),label = d... for n

fsolve(S,n);
Error, (in fsolve) left is in the equation, and is not solved for

Any suggestions on how to evaluate this would be fantastic. Thanks :)

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