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Help me on MLE of logistic distribution!!
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Help me on MLE of logistic distribution!!# Economics - 经济
i*g
1 楼
大虾救命！！！
How to find out the MLE of logistic distri.
f(x)=e^-1*(1+e^-1)^-2
it should be related to fisher information. but I do not
know how to calculate
the fisher information number.
also how to prove its variance=pi^2/3???
Thanks
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i*g
2 楼
sorry, typo, should be f(x)=e^-x*(1+e^-x)^-2
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c*e
3 楼
To consider MLE of a distribution, in the form of density,
there should have a parameter, so I think maybe u forgot to
include it. Is the density like this:
f(x,a)=e^(-(x-a))/[1+e^(-(x-a))]^2, it's the logistic
distribution.
For this distribution, consider L(x,a), which is
L(x,a)=f(x1,a)*f(x2,a)*...*f(xn,a) and take log both sides,
l(x,a)=log[f(x1,a)]+log[f(x2,a)]+...+log[f(xn,a)]
E{derivative of log[f(X,a)]}=Integral{ [derivative of
f(x,a)/f(x,a)]*f(x,a)dx
=Integral{

【在 i*****g 的大作中提到】
: sorry, typo, should be f(x)=e^-x*(1+e^-x)^-2
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