Print["Obtain the FI and corresponding variances"]
Print["    "]
Print["Mohammad Z. Raqab"]
Print["Department of Mathematics, University of Jordan"]
Print["March, 2012"]
Print["    "]
Print[alpha,"   ",FGR,"     ",FWe,"       ",VarGR,"      ",VarWe]

Print["------------------------------------------------------------"]
beta=5.0;theta=1; alpha=5.5543;lambda=1.6267;
f[x_]:=2*alpha*(lambda^2)*x*Exp[-(lambda*x)^2]*(1-Exp[-(lambda*x)^2])^(alpha-1);
r[x_]:=(x^2)*Exp[-(lambda*x)^2]/(1-Exp[-(lambda*x)^2]);
r1[x_]=Log[1-Exp[-(lambda*x)^2]];
a1=PolyGamma[2];
a2=PolyGamma[1,1];
f11=(a2+(a1^2))/(beta^2);
f22=(beta^2)/(theta^2);
f12=(1+PolyGamma[1])/theta;
g11=1/(alpha^2);
eta[y_]:=1+Log[1-y]-((alpha-1)*((1/y)-1)*Log[1-y]);
tau[y_]:=1+(alpha*Log[y]);
g12=(2/lambda)*NIntegrate[tau[y]*eta[y]*(y^(alpha-1)),{y,0,1},MaxRecursion->50];
g22=(4*alpha/lambda^2)*NIntegrate[(eta[y]^2)*(y^(alpha-1)),{y,0,1},MaxRecursion->50];
FIG={{g11,g12},{g12,g22}};
InFIG=Inverse[FIG];
FGR=Tr[FIG];
VarGR=Tr[InFIG];
FIW={{f11,f12},{f12,f22}};
InFIW=Inverse[FIW];
FWe=Tr[FIW];
VarWe=Tr[InFIW];
Print[beta,"   ",FGR,"   ",FWe,"    ",VarGR,"   ",VarWe]