How to Handle Estimating Parameters With MLE and Fmincon Errors
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Hi, I am trying to estimate the parameters of a distribution using mle and this is my log likelihood function
written in code as so filename (bgg.m)
function LL = bgg(p,x)
sum1 = 0;
sum2 = 0;
sum3 = 0;
sum4 = 0;
n = length(x);
for i = 1:n
a = exp(p(3) * x(i));
z = exp(-(p(2)/p(3)) * (a-1));
sum1 = sum1 + x(i);
sum2 = sum2 + a;
sum3 = sum3 + log(1 - z);
sum4 = sum4 + log(1 - (1-z)^p(1));
end
LL = n * log(p(1)) + n * log(p(2)) + n * p(2) / p(3) - n * log(beta(p(4),p(5)))...
+ p(3) * sum1 - p(2) / p(3) * sum2 + (p(1) * p(4) - 1) * sum3 + (p(5)-1) * sum4;
LL = double(-LL);
end
and I am trying to minimize the negative loglikelihood using fmincon as follows filename (calculate.m)
p = [];
x = [0.1, 0.2, 1, 1, 1, 1, 1, 2, 3, 6, 7, 11, 12, 18, 18, 18, 18, 18,...
21, 32, 36, 40, 45, 46, 47, 50, 55, 60, 63, 63, 67, 67, 67, 67, ...
72, 75, 79, 82, 82, 83, 84, 84, 84, 85, 85, 85, 85, 85, 86, 86];
lb = [2 0.003 0.05 0.1 0.008];
ub = [3 0.005 0.075 0.15 0.012];
p0 = lb + (ub-lb).*rand(1,length(lb));
i = 1;
options = optimoptions('fmincon','Algorithm',...
'interior-point','Display','iter','MaxFunEvals',1e+5,'MaxIter',500);
Ain = []; bin = []; Aeq = []; beq = [];
p = fmincon(@(p)bgg(p,x), p0,Ain,bin,Aeq,beq,lb,ub,@(p) confun(p), options);
y = bgg(p,x);
function[c,ceq]=confun(p)
c = [];
cin = [];
end
I have gotten multiple errors such as the most recent one is
Any suggestions for the problem I have or alternatives to using the code above? Thank you.
0 Comments
Answers (1)
Matt J
on 9 Jun 2022
Edited: Matt J
on 9 Jun 2022
The error is thrown because your confun tries to return a variable called ceq which you never create. You do create a variable called cin which is never used.
It is moot, however. Since you have no actual nonlinear constraints, there is no need to define a confun() at all:
p = fmincon(@(p)bgg(p,x), p0,Ain,bin,Aeq,beq,lb,ub, [] , options);
2 Comments
Matt J
on 10 Jun 2022
Are there closed form formulas for the mean and variance of the distribution? Maybe you could use them to minimize a simplified approximation to the LL.
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