How to find the maximum of mu by solving eqn

Hi, Can anyone please help me how to do this? Find the maximum of mu by solving eqn. Thank you so much.

      sigma = 1;
        syms mu

        n = 5;
        lambda = 1;

        U = normrnd(0,1,n,1);
        V = normrnd(0,1,n,1);
        W = (lambda/sqrt(1+lambda^2))*abs(U) + (1/sqrt(1+lambda^2))*V
        W_bar = sum(W)/n

        eqn = (W_bar - mu)/sigma == lambda*sum(normpdf(lambda*(W-mu)/sigma)/normcdf(lambda*(W-mu)/sigma));
        sol = solve(eqn,mu)

Answer 1

[Reza Bonyadi]

I think you are after

eqn = ((W_bar - mu)/sigma) - lambda*sum(normpdf(lambda*(W-mu)/sigma)./normcdf(lambda*(W-mu)/sigma))

rather than

eqn = ((W_bar - mu)/sigma) - lambda*sum(normpdf(lambda*(W-mu)/sigma)/normcdf(lambda*(W-mu)/sigma));

and then solve(eqn==0,mu). Note that the first equation returns a unique value while the second is actually a vector.

Does that make sense?

[Mikie]

Yes. Thank you so much.