Re: simple question

• To: mathgroup at smc.vnet.net
• Subject: [mg105247] Re: [mg105202] simple question
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Wed, 25 Nov 2009 02:34:56 -0500 (EST)
• References: <200911241048.FAA00724@smc.vnet.net>

```Hi Francisco,

The simplest is probably to use GatherBy:

Clear[gatherByPositions];
gatherByPositions[x_List, plist_List] :=
GatherBy[x, #[[plist]] &];

For example:

In[1]:= gatherByPositions[ejemplo1,{4,5}]

Out[1]=
{{{1,0,2,2,0}},{{0,1,1,1,2},{2,1,1,1,2}},{{2,0,0,1,1},{2,2,0,1,1}},{{1,1,0,2,2}},{{1,0,2,0,1},{0,1,1,0,1}}}

In[2]:= gatherByPositions[ejemplo1,{1,2}]

Out[2]=
{{{1,0,2,2,0},{1,0,2,0,1}},{{0,1,1,1,2},{0,1,1,0,1}},{{2,0,0,1,1}},{{1,1,0,2,2}},{{2,2,0,1,1}},{{2,1,1,1,2}}}

Regards,
Leonid

On Tue, Nov 24, 2009 at 1:48 PM, Francisco Gutierrez <fgutiers2002 at yahoo.com
> wrote:

> Dear List:
> I have the following list:
>
> ejemplo1={{1,0,2,2,0},{0,1,1,1,2},{2,0,0,1,1},{1,1,0,2,2},{1,0,2,0,1},{2,2,0,1,1},{2,1,1,1,2},{0,1,1,0,1}};
> 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:
>
> {{{1,1,0,2,2}},{{0,1,1,1,2},{2,1,1,1,2}},{{2,0,0,1,1},{2,2,0,1,1}},{{1,0,2,0,1},{0,1,1,0,1}},{{1,0,2,2,0}}},
> 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")?
> Fg
>
> --- On Mon, 11/23/09, Petri T=F6tterman <petri.totterman at hanken.fi> wrote:
>
>
> From: Petri T=F6tterman <petri.totterman at hanken.fi>
> Subject: [mg105202] [mg105180] ML estimators for Box-Cox Extreme Value
> distribution
> To: mathgroup at smc.vnet.net
> 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],
>    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
>
>

```

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