Errors in Estimating Parameters With MLE and fsolve

Hi, I am trying to estimate parameters of a distribution using mle, these are the objective functions

and in code (file name : sumbgg)

function F = sumbgg(p,x)

sum1 = 0;

sum2 = 0;

sum3 = 0;

sum4 = 0;

sum5 = 0;

sum6 = 0;

sum7 = 0;

sum8 = 0;

sum9 = 0;

sum10 = 0;

n = length(x);

for i = 1:n

e = exp(p(3) * x(i));

d = exp(-p(2) / p(3) * (e - 1));

c = 1 - d;

b = exp(p(3) * x(i) - 1);

a = c^p(1);

sum1 = sum1 + log(c);

sum2 = sum2 + a * log(c) / log(1 - a);

sum3 = sum3 + e;

sum4 = sum4 + b * d / c;

sum5 = sum5 + b * d / c * a / (1 - a);

sum6 = sum6 + x(i);

sum7 = sum7 + e * (1 - p(3)*x(i));

sum8 = sum8 + d * (p(3)*x(i) * e + e + 1) / c;

sum9 = sum9 + (a * d) * (p(3) * x(i) * e + e + 1) / (1 - a);

sum10 = sum10 + log(1 - a);

end

p3_2 = p(3)^2;

F = [n / p(1) + p(4) * sum1 - (p(5) - 1) * sum2;

n / p(2) + n / p(3) - 1 / p(3) * sum3 + ...

(p(1) * p(4) - 1) / p(3) * sum4 + p(1) * (p(5) - 1) / p(3) * sum5;

-n * p(2) / p3_2 + sum6 + p(2) * sum7 / p3_2 - ...

p(2) * (p(4) * p(1) - 1) * sum8 / p3_2 + ...

p(1) * p(2) * (p(5) - 1) * sum9 / p3_2;

-n * (psi(p(4)) + psi(p(4) + p(5))) + p(1) * sum1;

-n * (psi(p(4)) + psi(p(4) + p(5))) + p(1) * sum10];

F = double(F);

end

Then to find the parameters I used this code (filename: calc)

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];

p0 = [2 0.01 0.05 0.11 0.01];

i = 1;

options = optimoptions('fsolve');

p = fsolve(@(p)sumbgg(p,x), p0, options);

fprintf(p)

it then returned this error some errors such as

I have tried to fix it but nothing seems to work. Any suggestions for the problem I have or alternatives to using the code above? Thank you.

[Torsten]

The parameters a and b: do they have to be nonnegative in your model ? Or is it only a that has to be nonnegative and b has to be >= -a ?

[Natasha Davina]

@Torsten both a and b has to be nonnegative in my model. I am confused with the "X must be nonnegative" error message because all my x has a non negative value.

[Torsten]

a and b change in the course of the iteration since they are adjustable parameters.

Include the line

p(4:5) = p(4:5).^2

after the line

function F = sumbgg(p,x)

Remember that you will have to change the line

p0 = [2 0.01 0.05 0.11 0.01];

to

p0 = [2 0.01 0.05 sqrt[0.11,0.01]];

and the fitted paramters obtained

p = fsolve(@(p)sumbgg(p,x), p0, options);

to

p(4:5) = p(4:5).^2