# [R] sampling and gini index

Cesar Ortega cortega at unitec.edu
Mon Mar 10 18:41:57 CET 2003

```Thanks for you input,

However, I still need to do the following:

1. How can I work on the other 2 methods:Fixed systematic sampling and.

2. After I have done the 3 samplings methods, obtaining M(1000,or 2000,
or more, etc. for each sampling method) samples of n ( 3,4, 5, etc)
elements in a column,I need to take one by one each of the 1000, 2000,
etc. samples of each n elements and calculate in the 3 sampling methods:

a. PI(i)=n/N in simple and fixed sampling and i belogns to the sample.
PI(i) In MADOW is proprortional to an auxiliary variable Xi:PI(i)=RXi,
where r= MOD(TN,R), and TN=SUMi(Xi), i to N.
WE KNOW r, AND TN, BUT WE NEED TO FIND R FROM THE MODAL AND r.

ALSO CALCULATE:
ESTIMATED N= SUM {1/PI(i)};
ESTIMATED T(Y)= SUM {Yi/PI(i)};  i belongs to the sample.

GINMi=[SUMi{(Yi/PI(i))*[1/PI(i)+SUMj(2/PI(j)]}]/[(2*ESTIMATED
N*ESTIMATED T)].     i belongs to  M (1000,etc.) times, WHERE j=i+1

WE HAVE ONLY ONE VARIABLE Y, BUT WITH THE FIRST POSITION i AND THE
NEXT j, IN THE ASCENDING ORDER.

And last to get the errors as:

E1=  [SUMi {|GINP-GINMi |}]/[M] ; i belongs M

E2= SQRT[SUMi {|GINP-GINMi |}]/[M]; i belongs TO M

Cesar
----- Original Message -----
From: Achim Zeileis <zeileis at ci.tuwien.ac.at>
Date: Monday, March 10, 2003 6:03 pm
Subject: Re: [R] sampling and gini index

> On Monday 10 March 2003 16:34, Carlos Ortega wrote:
>
> > Cesar,
> >
> > For the first part, please check the function included. For the
> > sampling, please check "?sample".
> >
> > Regards,
> > Carlos.
> >
> > g.index<-function(y) {
> > 	sum.res<-0
> > 	y.lg<-length(y)
> > 	y.mean<-mean(y)
> >
> > 	for (i in 1:y.lg) {
> >   	        for (j in 1:y.lg) {
> >     	                ratio.res<-abs(y[i]-y[j]) / (2 * y.lg^2
*
> y.mean)>     	                sum.res<-sum.res+ratio.res
> >   	        }
> > 	}
> >   	return(sum.res)
> >  }
> >
> >  y<-rnorm(284)
> >  g.index(y)
> >
>
> A more efficient implementation of the Gini index can be found in
> the
> ineq package. See
>  help(Gini)
>  help(ineq)
> Z
>
> >
> >
> >
> > -----Mensaje original-----
> > De: r-help-bounces at stat.math.ethz.ch
> > [mailto:r-help-bounces at stat.math.ethz.ch]En nombre de Cesar Ortega
> > Enviado el: lunes, 10 de marzo de 2003 12:17
> > Para: r-help at stat.math.ethz.ch
> > CC: r-help at stat.math.ethz.ch
> > Asunto: [R] sampling and gini index
> >
> >
> > Hi there,
> >
> >
> > I am new in R, and I was wondering if I could do the following
> in R,
> > since I have tried in SPSS and I have only done part of it.  I
> > would appreciate any help to build this routine in R, if possible:
> >
> >
> >
> > I have a column of 284 elements Y, [...]
> >
> > > Iam reading these as 284 cases with a single
> > > variable, which I will call Y
> > >
> > > >  where first I need to calculate:
> > > >
> > > >GINP=[SUMi SUMj {|Yi - Yj|}]/[2(N**2)*MEAN(Y)], where Yi and Yj
> > >
> > > are
> > >
> > > >the 284 elements, 0<Y1<=Y2...<=Y284.  j: is the next position of
> > > > i.
> > >
> > > Here, I am doing a calculation to yield a single number.
> > > Calculating
> >
> >  (I assume that N=284)
> >
> > > >Next, I need to take the 284 numbers and resampling them in
> > >
> > > [groups
> > >
> > > >of] n data (like 3, 4, 5,  etc) for M number of samples ( like
> > >
> > > 1000,
> > >
> > > >2000, etc, one at a time) in 3 sampling methods:
> > > >
> > > >1. Simple sampling without replacing.
> > > >2. Fixed systematic sampling.
> > > >3. Proportional sampling Madow.
> >
> > SIMPLE SAMPLING WITHOUT REPLACING THE POSITION VALUE, FOR
> INTANCE 3,
> > IF WE HAVE THE POSITION 3,7,9 WITH ITS VALUES, WE COULD HAVE 3,7,10,
> > BUT WE COULD NOT HAVE THE POSITIONS 9,3,7 AGAIN.  SO THIS IS A
> > COMBINATION, AND IF WE TAKE 3 COMBINATIONS OUT 284 WE HAVE
> > 284!/(3!*281!). AND WE NEED TO START FROM 1000 GROUPS OF
> > COMBINATIONS. IT IS LIKE
> > IF WE HAVE 1,2,3,4,5 AND WE WANT COMBINATIONS OF 2, WE COULD
> HAVE IN
> > 1,2 AND 1,3 AND 1,4 AND 1,5 AND 2,3 AND 2,4, ETC, BUT IN RANDOM
> > ORDER.
> >
> > > >After I have the M(1000, 2000) samples of n ( 3,4, 5)elements in
> > >
> > > a column,
> > >
> > > >I need to take one by one each of the 1000 samples of each n
> > >
> > > elements
> > >
> > > >and calculate:
> > > >
> > > >PI(i)=n/N in simple and fixed sampling and i belogns to the
> > >
> > > sample. In
> > >
> > > >MADOW  PI(i) is proprortional to an auxiliary variable Xi:PI(i)=
> > >
> > > RXi,
> > >
> > > >where r= MOD(TN,R), and TN=SUMi(Xi), i to N.
> >
> > WE KNOW r, AND TN, BUT WE NEED TO FIND R FROM THE MODAL AND r.
> >
> > AND CALCULATE:
> > > >ESTIMATED N= SUM {1/PI(i)};
> > > >ESTIMATED T(Y)= SUM {Yi/PI(i)};  i belongs to the sample.
> >
> > GINMi=[SUMi{(Yi/PI(i))*[1/PI(i)+SUMj(2/PI(j)]}]/[(2*ESTIMATED
> > N*ESTIMATED T)].     i belongs to  M (1000) times, WHERE j=i+1
> >
> > WE HAVE ONLY ONE VARIABLE Y, BUT WITH THE FIRST POSITION i AND THE
> > NEXT j, IN THE ASCENDING ORDER.
> >
> > > >And last to get the errors as:
> > > >
> > > >E1=  [SUMi {|GINP-GINMi |}]/[M] ; i belongs M
> > > >
> > > >E2= SQRT[SUMi {|GINP-GINMi |}]/[M]; i belongs TO M
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://www.stat.math.ethz.ch/mailman/listinfo/r-help
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>

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