centrum maten-huur niet-sociale woning- olivier bosiers

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 18 Aug 2009 07:02:34 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/18/t1250600646kv1bwtc4e38735m.htm/, Retrieved Tue, 18 Aug 2009 15:04:06 +0200

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/2009/Aug/18/t1250600646kv1bwtc4e38735m.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

102,2 102,4 102,4 102,5 102,5 102,6 102,8 102,9 102,9 103,1 103,2 103,3 103,6 103,7 103,8 104 104 104,1 104,2 104,3 104,4 104,5 104,7 104,7 104,9 105 105,2 105,3 105,4 105,5 105,7 105,8 105,9 106 106,1 106,2 106,6 106,8 107 107,1 107,3 107,4 107,6 107,7 107,9 108,2 108,3 108,5 108,92 109,23 109,41 109,65 109,91 110,01 110,2 110,49 110,57 110,72 110,94 111,09 111,28 111,41 111,62 111,76 111,89 112,04 112,12 112,3 112,47 112,59 112,78 112,73 112,99 113,1 113,33 113,38 113,68 113,65 113,81 113,88 114,02 114,25 114,28 114,38 114,73 114,97 115,05 115,29 115,37 115,54 115,76 115,92 116,02 116,21 116,26 116,51

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 108.944895833333 0.452261398632251 240.889220620662 Geometric Mean 108.855834421046 Harmonic Mean 108.766954368993 Quadratic Mean 109.034039013244 Winsorized Mean ( 1 / 32 ) 108.944375 0.451487570803353 241.300939483562 Winsorized Mean ( 2 / 32 ) 108.943333333333 0.451310461922761 241.393325714613 Winsorized Mean ( 3 / 32 ) 108.940520833333 0.449841525940351 242.175331869603 Winsorized Mean ( 4 / 32 ) 108.936354166667 0.449155423803691 242.535987307322 Winsorized Mean ( 5 / 32 ) 108.933229166667 0.447022446716312 243.686262215368 Winsorized Mean ( 6 / 32 ) 108.931979166667 0.442994807595794 245.898997683197 Winsorized Mean ( 7 / 32 ) 108.926875 0.440009327864144 247.555831438264 Winsorized Mean ( 8 / 32 ) 108.920208333333 0.438986396783172 248.11750234514 Winsorized Mean ( 9 / 32 ) 108.916458333333 0.432910564159241 251.591130710475 Winsorized Mean ( 10 / 32 ) 108.918541666667 0.430206804083769 253.17717114827 Winsorized Mean ( 11 / 32 ) 108.9025 0.424586589437096 256.490672831612 Winsorized Mean ( 12 / 32 ) 108.89625 0.413234201733661 263.521870995049 Winsorized Mean ( 13 / 32 ) 108.89625 0.409533598915096 265.903091439821 Winsorized Mean ( 14 / 32 ) 108.906458333333 0.406991636923395 267.588934152551 Winsorized Mean ( 15 / 32 ) 108.901770833333 0.397985469704999 273.632529634952 Winsorized Mean ( 16 / 32 ) 108.8784375 0.394850441598856 275.746019326006 Winsorized Mean ( 17 / 32 ) 108.88375 0.390909708525253 278.539385503561 Winsorized Mean ( 18 / 32 ) 108.878125 0.385288064722984 282.588886002170 Winsorized Mean ( 19 / 32 ) 108.891979166667 0.381992313570588 285.06327299841 Winsorized Mean ( 20 / 32 ) 108.8565625 0.3720728396231 292.567881628417 Winsorized Mean ( 21 / 32 ) 108.8675 0.367929037065287 295.892656008778 Winsorized Mean ( 22 / 32 ) 108.860625 0.355569003237904 306.158928389952 Winsorized Mean ( 23 / 32 ) 108.834270833333 0.352278882520642 308.943499691487 Winsorized Mean ( 24 / 32 ) 108.831770833333 0.339671345115833 320.403155574457 Winsorized Mean ( 25 / 32 ) 108.844791666667 0.334919733090339 324.987693804555 Winsorized Mean ( 26 / 32 ) 108.861041666667 0.323809509167565 336.188526231122 Winsorized Mean ( 27 / 32 ) 108.855416666667 0.316397308687107 344.046594828392 Winsorized Mean ( 28 / 32 ) 108.835 0.307027736046362 354.479375060649 Winsorized Mean ( 29 / 32 ) 108.810833333333 0.297058335972516 366.294495581502 Winsorized Mean ( 30 / 32 ) 108.848333333333 0.286850932720009 379.459576098288 Winsorized Mean ( 31 / 32 ) 108.8321875 0.277481910392095 392.213630597451 Winsorized Mean ( 32 / 32 ) 108.8221875 0.268648673396415 405.072491608486 Trimmed Mean ( 1 / 32 ) 108.936170212766 0.449035752459167 242.600215275001 Trimmed Mean ( 2 / 32 ) 108.927608695652 0.446131896020721 244.160100784619 Trimmed Mean ( 3 / 32 ) 108.919222222222 0.442817650230036 245.968565538525 Trimmed Mean ( 4 / 32 ) 108.911477272727 0.439528683274983 247.791512629425 Trimmed Mean ( 5 / 32 ) 108.904534883721 0.435873783390609 249.853372773572 Trimmed Mean ( 6 / 32 ) 108.897976190476 0.432150481236157 251.990871047918 Trimmed Mean ( 7 / 32 ) 108.891341463415 0.428709215850731 253.998135419904 Trimmed Mean ( 8 / 32 ) 108.88525 0.425245944287434 256.052412639594 Trimmed Mean ( 9 / 32 ) 108.879871794872 0.421299643638501 258.438081871004 Trimmed Mean ( 10 / 32 ) 108.874736842105 0.417710109907271 260.646640480583 Trimmed Mean ( 11 / 32 ) 108.869054054054 0.413845135239567 263.067134982828 Trimmed Mean ( 12 / 32 ) 108.865 0.41011811726568 265.447917116707 Trimmed Mean ( 13 / 32 ) 108.861428571429 0.407407106139666 267.205522267226 Trimmed Mean ( 14 / 32 ) 108.857647058824 0.404562387147214 269.07505620193 Trimmed Mean ( 15 / 32 ) 108.852575757576 0.401345308230345 271.219255651798 Trimmed Mean ( 16 / 32 ) 108.84765625 0.398650236449454 273.040490881036 Trimmed Mean ( 17 / 32 ) 108.844677419355 0.395622779015084 275.122372099825 Trimmed Mean ( 18 / 32 ) 108.841 0.392292098308748 277.448871565948 Trimmed Mean ( 19 / 32 ) 108.837586206897 0.388828441069688 279.911587504963 Trimmed Mean ( 20 / 32 ) 108.832678571429 0.384807127525269 282.823967610324 Trimmed Mean ( 21 / 32 ) 108.830555555556 0.381136574624096 285.542146310393 Trimmed Mean ( 22 / 32 ) 108.827307692308 0.376911629862808 288.734278992452 Trimmed Mean ( 23 / 32 ) 108.8244 0.373323972671765 291.501237440439 Trimmed Mean ( 24 / 32 ) 108.823541666667 0.368949713267958 294.954943053801 Trimmed Mean ( 25 / 32 ) 108.822826086957 0.365179945457835 297.997815708425 Trimmed Mean ( 26 / 32 ) 108.820909090909 0.360707230228175 301.687629111486 Trimmed Mean ( 27 / 32 ) 108.817380952381 0.356497684772046 305.240077567296 Trimmed Mean ( 28 / 32 ) 108.814 0.351859492644582 309.254126362066 Trimmed Mean ( 29 / 32 ) 108.812105263158 0.347033999977058 313.548831729316 Trimmed Mean ( 30 / 32 ) 108.812222222222 0.34204801276065 318.119732209537 Trimmed Mean ( 31 / 32 ) 108.808823529412 0.33685019036615 323.018441554504 Trimmed Mean ( 32 / 32 ) 108.8065625 0.331121508668682 328.600104950811 Median 108.71 Midrange 109.355 Midmean - Weighted Average at Xnp 108.6586 Midmean - Weighted Average at X(n+1)p 108.823541666667 Midmean - Empirical Distribution Function 108.6586 Midmean - Empirical Distribution Function - Averaging 108.823541666667 Midmean - Empirical Distribution Function - Interpolation 108.823541666667 Midmean - Closest Observation 108.6586 Midmean - True Basic - Statistics Graphics Toolkit 108.823541666667 Midmean - MS Excel (old versions) 108.743529411765 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600646kv1bwtc4e38735m/1wuan1250600549.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600646kv1bwtc4e38735m/1wuan1250600549.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600646kv1bwtc4e38735m/2ek021250600549.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250600646kv1bwtc4e38735m/2ek021250600549.ps (open in new window)

Parameters (Session):

par1 = 0 ;

Parameters (R input):

par1 = 0 ;

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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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