Maximum Likelihood Estimation function

syms a
logL=100.*log(a)+sum(log(exp(a.*c2))+sum(log((1+exp(a.*c2)).^-2)));
j = fplot(logL)
hold on 
%%
m=100/a;
o=sum(c);
p=2*exp(a.*c);
q=exp(a.*c)+1;
dlog=m+o-p.*c.*(q.^-1);
k=fplot(dlog);
hline.Color = 'k';

c is a matrix of data

I am trying to find the maximum of the estimator is there another method except plotting the graphs of the log functions?

Answer 1

[Torsten]

x = your data vector
fun = @(a) n/a + sum(x) - 2*a*sum(exp(a*x)./(exp(a*x)+1);
a = fzero(fun,1)

[Jane Smith]

This worked perfectly! Thank you.

[Torsten]

I think there is an error in your derivative of L with respect to a. In my opinion, the function must be

fun = @(a) n/a + sum(x) - 2*sum(x.*exp(a*x)./(exp(a*x)+1))

[Jane Smith]

Yes you are correct.

Answer 2

[John D'Errico]

Is there another way? Why not negate the function, and then use a tool like fminbnd? Or fminsearch. Or fmincon or fminunc, or ...

[Jane Smith]

I am getting errors when trying with those functions.

Error using fcnchk

FUN must be a function, a valid character vector expression, or an inline function object.

I have been trying it on various softwares. The function f(x) is made up so i am getting confused were my mistake is in finding the estimate.

[David Randolph]

@John D'Errico wrong again!