How to Handle Estimating Parameters With MLE and Fmincon Errors

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.

Answer 1

[Matt J]

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);

[Natasha Davina]

@Matt J You're correct thank you very much! If i may ask a followup question, in the example I know the results I wanted and used that as a way of setting the lb, ub, and p0. However if I used random data for X do you know how should I determine the initial values?

[Matt J]

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.