Re: MLE Problem

Brenneman wrote:
Hi,

I am having a bugger of a time with a problem that doesn't seem too
hard.

I want to find an MLE for the non-centrality parameter of a
non-central chi-squared distbtn.

Normally, this would be a bear, but in this case, the problem is not
too bad, because the distribution has only 2 degrees of freedom, so
my
pdf is:

(i) f(z) = z * exp[-(z^2 + c^2)/2] * I_0(c*z)
where c is my non-centrality param and I_0 is modified Bessel
function
of zero order.

The log function is:
(ii) Ln(f) = ln(z) - (z^2 + c^2)/2 + ln[ I_0(cz) ]

and using the fact that:
(iii) d/dx I_0(x) = I_1(x)

gives us the derivative of the log liklihood function (I'll call F)
as: (iv) F(z) = 1/z - z + c * I_1(cz)/I_0(cz)


? Why are you taking the derivative with respect to z, and not c?

David Jones


.

Relevant Pages

  • MLE Problem
    ... I want to find an MLE for the non-centrality parameter of a non-central ... where c is my non-centrality param and I_0 is modified Bessel function ...
    (sci.stat.edu)
  • Probability Theory Problem
    ... I want to find an MLE for the non-centrality parameter of a non-central ... where c is my non-centrality param and I_0 is modified Bessel function ... of eqn has a constant in it, which the RHS doesn't. ...
    (sci.math)