Solving a nonlinear system : 3 equations 3 variables.

Irad Chammem

2017 1 14

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Hi guys,

English is not my native language so forgive me in advance if I make some mistakes. I'm new to matlab and to statistics, using the method of moments I want to find the estimators for the burr type XII distribution but the equations are really complicated. I tried to use the fsolve command but I had a lot of errors. I was wondering if there was another solution. PS : varemp is the empirical variation, esp is the empirical mean.

Thank you.

    %LOI de Burr de type XII
%Estimation par la méthode des moments
mord3=0; %moment d'ordre 3
for i=1:length(A)
mord3=mord3+A(i)^3;
end
mord3=mord3/length(A);
Ep=@(lamda,alpha,gam) (lamda*gamma(1+1/gam)*gamma(alpha-1/gam))/gamma(alpha)-esp; %espérance de burr
Vr=@(lamda,alpha,gam) lamda^2*gamma(1+2/gam)*gamma(alpha-2/gam)/gamma(alpha) - (lamda*gamma(1+1/gam)*gamma(alpha-1/gam)/gamma(alpha))^2 - varemp; %variance de burr
Mmord3=@(lamda,alpha,gam) lamda^3*gamma(1+3/gam)*gamma(alpha-3/gam)/gamma(alpha)- mord3; %moment d'ordre 3 de burr