ML estimators for Box-Cox Extreme Value distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg105180] ML estimators for Box-Cox Extreme Value distribution
- From: Petri Tötterman <petri.totterman at hanken.fi>
- Date: Mon, 23 Nov 2009 06:53:58 -0500 (EST)
Dear all,
I have a set of data, and I want to fit a distribution on this data. I
am particularily interested in the Box-Cox General Extreme Value
distribution, for which I have the CDF and PDF:
---
BoxCoxGEVDistribution /:
CDF[BoxCoxGEVDistribution[\[Mu]_, \[Sigma]_, \[Xi]_, \[Phi]_], x_] :=
1 + (((Exp[-(1 + \[Xi] ( (x - \
\[Mu])/\[Sigma]))^(-1/\[Xi])])^\[Phi]) - 1)/\[Phi];
BoxCoxGEVDistribution /:
PDF[BoxCoxGEVDistribution[\[Mu]_, \[Sigma]_, \[Xi]_, \[Phi]_], x_] =
D[CDF[BoxCoxGEVDistribution[\[Mu], \[Sigma], \[Xi], \[Phi]], x],
x];
---
I do also have a Log likelihood function from (Bali, 2007):
---
LLdBoxCoxGEV[\[Mu]_, \[Sigma]_, \[Xi]_, \[Phi]_, M_] :=
Module[{k = Length[M]}, -k Log[\[Sigma]] -
k ((1 + \[Xi])/\[Xi]) Sum[
Log[1 + \[Xi] ((M[[i]] - \[Mu])/\[Sigma])], {i, 1, k}] -
k \[Phi] Sum[(1 + \[Xi] ((M[[i]] - \[Mu])/\[Sigma]))^(-(
1/\[Xi])), {i, 1, k}] ];
---
Obviously, \[Mu]_, \[Sigma]_, \[Xi]_, \[Phi]_ are parameters which I
need to estimate, and M is a list of values from the dataset,
exceeding a predefined limit.
I would be grateful for advice, how should I continue to find the
Maximum Likelihood estimators for this distribution, using Mathematica?
Best regards,
/petri