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Wisselkoers Robustness Lordina Febiri

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 14 Mar 2010 14:38:36 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/14/t1268599299oxy8ukx4jqvne3i.htm/, Retrieved Sun, 14 Mar 2010 21:41:41 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Mar/14/t1268599299oxy8ukx4jqvne3i.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
0,8833 0,87 0,8758 0,8858 0,917 0,9554 0,9922 0,9778 0,9808 0,9811 1,0014 1,0183 1,0622 1,0773 1,0807 1,0848 1,1582 1,1663 1,1372 1,1139 1,1222 1,1692 1,1702 1,2286 1,2613 1,2646 1,2262 1,1985 1,2007 1,2138 1,2266 1,2176 1,2218 1,249 1,2991 1,3408 1,3119 1,3014 1,3201 1,2938 1,2694 1,2165 1,2037 1,2292 1,2256 1,2015 1,1786 1,1856 1,2103 1,1938 1,202 1,2271 1,277 1,265 1,2684 1,2811 1,2727 1,2611 1,2881 1,3213 1,2999 1,3074 1,3242 1,3516 1,3511 1,3419 1,3716 1,3622 1,3896 1,4227 1,4684 1,457 1,4718 1,4748 1,5527 1,575 1,5557 1,5553 1,577 1,4975 1,4369 1,3322 1,2732 1,3449 1,3239 1,2785 1,305 1,319 1,365 1,4016 1,4088 1,4268 1,4562 1,4816 1,4914 1,4614 1,4272
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.258514432989690.016885932247928774.5303495543793
Geometric Mean1.24701367517144
Harmonic Mean1.23481514243779
Quadratic Mean1.26934294420381
Winsorized Mean ( 1 / 32 )1.258553608247420.0168676599832874.6134087060658
Winsorized Mean ( 2 / 32 )1.258310309278350.016755681480184975.0975309936759
Winsorized Mean ( 3 / 32 )1.258375257731960.016735416346472975.1923484710416
Winsorized Mean ( 4 / 32 )1.259554639175260.016426531349462376.6780650387574
Winsorized Mean ( 5 / 32 )1.258688659793810.015516050322286081.1217180693164
Winsorized Mean ( 6 / 32 )1.259696907216490.015180662851129982.9803625552977
Winsorized Mean ( 7 / 32 )1.259206185567010.015028096882416283.7901296098483
Winsorized Mean ( 8 / 32 )1.258670103092780.014937823826807384.2606070125145
Winsorized Mean ( 9 / 32 )1.259421649484540.014698692158638085.6825652168248
Winsorized Mean ( 10 / 32 )1.260019587628870.014467899251830487.0907078973095
Winsorized Mean ( 11 / 32 )1.261142268041240.013997506668857190.0976365203055
Winsorized Mean ( 12 / 32 )1.266028865979380.012978548912347597.5477978724505
Winsorized Mean ( 13 / 32 )1.267945360824740.0126373870894969100.332873547773
Winsorized Mean ( 14 / 32 )1.265650515463920.0121388688638272104.264287691207
Winsorized Mean ( 15 / 32 )1.264784536082470.011820679007196106.997621313676
Winsorized Mean ( 16 / 32 )1.269518556701030.0110782929457432114.595142312863
Winsorized Mean ( 17 / 32 )1.270254639175260.0107614531832244118.037463672230
Winsorized Mean ( 18 / 32 )1.270458762886600.00999195775758778127.148131898559
Winsorized Mean ( 19 / 32 )1.273161855670100.00923494972832818137.863431109396
Winsorized Mean ( 20 / 32 )1.272357731958760.00866644505173446146.814261714395
Winsorized Mean ( 21 / 32 )1.269088659793810.00805232763891286157.605194013833
Winsorized Mean ( 22 / 32 )1.267818556701030.00782685088529905161.983226112349
Winsorized Mean ( 23 / 32 )1.269146391752580.00748598878264012169.536240115094
Winsorized Mean ( 24 / 32 )1.268255670103090.00693513732082214182.873908825895
Winsorized Mean ( 25 / 32 )1.270240206185570.00666132695194625190.688764468232
Winsorized Mean ( 26 / 32 )1.269838144329900.00630355805598402201.447838356058
Winsorized Mean ( 27 / 32 )1.269615463917530.00612849895504793207.165812253548
Winsorized Mean ( 28 / 32 )1.269528865979380.00606252926424419209.405812433246
Winsorized Mean ( 29 / 32 )1.267107216494850.00573539573849186220.927600163827
Winsorized Mean ( 30 / 32 )1.265158762886600.00538537433898512234.924943606616
Winsorized Mean ( 31 / 32 )1.267172164948450.00512705677910938247.153916865452
Winsorized Mean ( 32 / 32 )1.267469072164950.0048958520386039258.886310732213
Trimmed Mean ( 1 / 32 )1.259251578947370.01640318659555576.7687163473837
Trimmed Mean ( 2 / 32 )1.259979569892470.015873965940129679.3739620359915
Trimmed Mean ( 3 / 32 )1.260869230769230.015337293221138482.2093711445416
Trimmed Mean ( 4 / 32 )1.261775280898880.014729061529041885.6656942067211
Trimmed Mean ( 5 / 32 )1.262394252873560.014138235258373789.2893794595671
Trimmed Mean ( 6 / 32 )1.263240.013730059255912592.0054295800667
Trimmed Mean ( 7 / 32 )1.263240.013346911817127894.6466131872474
Trimmed Mean ( 8 / 32 )1.264738271604940.012938753346923997.7480780175487
Trimmed Mean ( 9 / 32 )1.265669620253160.0124829019517655101.392258398229
Trimmed Mean ( 10 / 32 )1.266544155844160.0120011255586148105.535447459342
Trimmed Mean ( 11 / 32 )1.2673880.0114824227534213110.376357604702
Trimmed Mean ( 12 / 32 )1.268142465753420.0109657211008244115.646062314870
Trimmed Mean ( 13 / 32 )1.268383098591550.0105572584595029120.143226904693
Trimmed Mean ( 14 / 32 )1.268383098591550.0101370275628766125.123769342068
Trimmed Mean ( 15 / 32 )1.268717910447760.00972852351188358130.412174971669
Trimmed Mean ( 16 / 32 )1.269109230769230.00929697265736089136.507794261868
Trimmed Mean ( 17 / 32 )1.269069841269840.00891743737712319142.313288851965
Trimmed Mean ( 18 / 32 )1.268959016393440.00851604219916586149.008070499901
Trimmed Mean ( 19 / 32 )1.268822033898310.00817182944156054155.267806673166
Trimmed Mean ( 20 / 32 )1.268433333333330.00788865986524372160.791991922717
Trimmed Mean ( 21 / 32 )1.268087272727270.00764362019335333165.901397590368
Trimmed Mean ( 22 / 32 )1.2680.00745153815663953170.166209089351
Trimmed Mean ( 23 / 32 )1.268015686274510.00725053635476418174.885777304092
Trimmed Mean ( 24 / 32 )1.267918367346940.00705866734152737179.625743217498
Trimmed Mean ( 25 / 32 )1.267918367346940.00691593919370417183.332781251341
Trimmed Mean ( 26 / 32 )1.267686666666670.00677912094655943186.998679719684
Trimmed Mean ( 27 / 32 )1.26750.00666571034115341190.152277121102
Trimmed Mean ( 28 / 32 )1.26750.00654462315240684193.670433038435
Trimmed Mean ( 29 / 32 )1.267117948717950.00638990946251996198.299828213566
Trimmed Mean ( 30 / 32 )1.267118918918920.00625025145180403202.73087070012
Trimmed Mean ( 31 / 32 )1.267118918918920.00613257454811886206.621038028409
Trimmed Mean ( 32 / 32 )1.267312121212120.00602248903664511210.429959025395
Median1.2694
Midrange1.2235
Midmean - Weighted Average at Xnp1.266175
Midmean - Weighted Average at X(n+1)p1.26791836734694
Midmean - Empirical Distribution Function1.26791836734694
Midmean - Empirical Distribution Function - Averaging1.26791836734694
Midmean - Empirical Distribution Function - Interpolation1.26791836734694
Midmean - Closest Observation1.266132
Midmean - True Basic - Statistics Graphics Toolkit1.26791836734694
Midmean - MS Excel (old versions)1.26791836734694
Number of observations97
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Mar/14/t1268599299oxy8ukx4jqvne3i/1lba71268599114.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/14/t1268599299oxy8ukx4jqvne3i/1lba71268599114.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Mar/14/t1268599299oxy8ukx4jqvne3i/24gug1268599114.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/14/t1268599299oxy8ukx4jqvne3i/24gug1268599114.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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