Maximum likelihood estimatior

• To: mathgroup at smc.vnet.net
• Subject: [mg121249] Maximum likelihood estimatior
• From: "jeanni laus" <jeanni.laus at gmx.de>
• Date: Tue, 6 Sep 2011 03:56:39 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi
I have some trouble calculating the maximum likelihood estimators for some distribution functions e.g. Gumbel, Log-Normal Distribution.
I tried to use the SMLE package. Everything worked fine for the examples given in the Symbolic maximum likelihood estimation with Mathematica paper. But for my distribution functions I can't calculate the estimators.

SuperLog[On]
func=PDF[GumbelDistribution[\[Alpha], \[Beta]], Subscript[x, i]]
L= \!\(\*UnderoverscriptBox[\(\[Product]\), \(i = 1\), \(n\)]func\)
LogL=Log[L]
scorea = \!\(\*SubscriptBox[\(\[PartialD]\), \(\[Alpha]\)]LogL\)
scoreb = \!\(\*SubscriptBox[\(\[PartialD]\), \(\[Beta]\)]LogL\)
Assuming[\[Beta] > 0, Solve[scorea == 0, \[Alpha]]]
Assuming[\[Beta] > 0, Solve[scoreb == 0, \[Beta]]]

Jeanni

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```

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