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simple question

  • To: mathgroup at
  • Subject: [mg105202] simple question
  • From: Francisco Gutierrez <fgutiers2002 at>
  • Date: Tue, 24 Nov 2009 05:48:51 -0500 (EST)

Dear List:
I have the following list:
I want to group it, so that the sublists of ejemplo1 that have identical values at positions 4 and 5 are gathered together. So I did the following code:
Split[ Sort[ejemplo1,#1[[4]]>=#2[[4]] && #1[[5]]>=#2[[5]] &],Take[#1,{4,5}]==Take[#2,{4,5}]&]
Works! The output in effect is:
precisely what I wanted.
Now, how can I create a function for the general case (instead of fixed positions 4 and 5, an arbitrary number of positions that act as "gathering parameter")?

--- On Mon, 11/23/09, Petri T=F6tterman <petri.totterman at> wrote:

From: Petri T=F6tterman <petri.totterman at>
Subject: [mg105202] [mg105180] ML estimators for Box-Cox Extreme Value distribution
To: mathgroup at
Date: Monday, November 23, 2009, 6:53 AM

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],

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,

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