How to find the maximum of mu by solving eqn

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Mikie
Mikie 2017-10-25
评论： Mikie 2017-10-25
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)

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采纳的回答

Reza Bonyadi
Reza Bonyadi 2017-10-25
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?

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