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R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Fri, 30 Nov 2007 17:57:18 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/01/t1196469974xltr73myfjjc060.htm/, Retrieved Sat, 01 Dec 2007 01:46:16 +0100
 
User-defined keywords:
 
Dataseries X:
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0.0869999446951916 -10.6424981202654 -2.6399168772836 13.7558429695092 10.7917666643614 5.27149534693457 6.26236873355704 0.0808879526036979 5.31218885914988 2.90275581292451 -2.1172733192881 -3.64795342124611 0.445213929707559 -0.697430413548686 0.633164712122324 -2.77874271382277 -6.11406765778734 -4.52212849113731 -10.6625189768281 10.9360837352993 7.33386844796123 -2.97571273751731 -3.64406701373923 0.0448714919763739 7.49173211393255 -9.1792897906477 11.5266884118631 1.61098394547433 4.57870993463288 5.01644339045671 -0.739762573720376 2.99782981858344 0.181030920499866 8.17507409392053 -6.46104702251396 4.54039824269657 2.64048714448227 -7.80288662648454 3.21235406248661 2.03519748122038 1.41666175824866 3.50724430172785 4.6229155092342 -4.13119111238983 -9.93147203691156 -1.99346515298457 -6.89246008626617 2.27344896477510 -11.445659865243 5.7145163962 -0.355875692765096 3.33498288070947 3.42283523249355 0.898139693377297 -1.11764786593179 -1.27360973509249 -2.73969923992811 3.21891406919454 2.21035873629311 -2.51589341895093 -0.596534223613034 8.29299003060472 1.64570357053192 -5.70825095122994 6.39727671299076 2.6510116283072 -1.54085890770451 7.39162471304801 0.231112187175277 4.04923538236955 0.101743268713107 -8.99960636951208 -1.69889302077304
 
Text written by user:
 
Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5983389008482080.643619165121780.92964742703862
Geometric MeanNaN
Harmonic Mean1.13004681640811
Quadratic Mean5.49396894599308
Winsorized Mean ( 1 / 24 )0.5785304944203830.6328922265432810.914105862194248
Winsorized Mean ( 2 / 24 )0.5628980609956950.628959383362250.89496726797618
Winsorized Mean ( 3 / 24 )0.5861874724648430.6205471463033040.944630034892358
Winsorized Mean ( 4 / 24 )0.4904836704104420.5824753505001120.842067685764409
Winsorized Mean ( 5 / 24 )0.4947143200304030.5781565770637240.855675330276276
Winsorized Mean ( 6 / 24 )0.5369097526089970.5463378387691270.982743120664367
Winsorized Mean ( 7 / 24 )0.6146115878875840.5267254146494431.16685386881632
Winsorized Mean ( 8 / 24 )0.6555602781522880.5163858169778081.26951642860567
Winsorized Mean ( 9 / 24 )0.5828683420948280.488274373826961.19373117521296
Winsorized Mean ( 10 / 24 )0.6199791266323180.4747783114894411.30582866072244
Winsorized Mean ( 11 / 24 )0.7161568163595980.4295365875418071.66727779921633
Winsorized Mean ( 12 / 24 )0.7142844615701230.4082728281286061.74952730712984
Winsorized Mean ( 13 / 24 )0.7930936989135390.3932857885386272.01658367026309
Winsorized Mean ( 14 / 24 )0.7449249634944470.3855359116695731.93218048162759
Winsorized Mean ( 15 / 24 )0.801396140549120.3520976339859172.27606227135617
Winsorized Mean ( 16 / 24 )0.8348787595284560.3442719508259292.42505599868224
Winsorized Mean ( 17 / 24 )0.8350491745050580.3416026139963662.44450463869677
Winsorized Mean ( 18 / 24 )0.7385443942545760.320179417847152.30665793329398
Winsorized Mean ( 19 / 24 )0.6297583007768830.295745963087062.1293893387532
Winsorized Mean ( 20 / 24 )0.7158435145929190.2767729717057132.58639241462516
Winsorized Mean ( 21 / 24 )0.7261869680848160.2683106765080632.70651536321922
Winsorized Mean ( 22 / 24 )0.779982489390640.2512539866736993.10435866000246
Winsorized Mean ( 23 / 24 )0.8277072078330210.2442086252520483.38934469238646
Winsorized Mean ( 24 / 24 )0.8450414309701770.2229738273167833.78986826005193
Trimmed Mean ( 1 / 24 )0.5826557275725770.6116047017825830.952667181717814
Trimmed Mean ( 2 / 24 )0.5870201046756230.586297903528381.00123179895902
Trimmed Mean ( 3 / 24 )0.6001612180236430.5585639052121541.07447189555811
Trimmed Mean ( 4 / 24 )0.6053924150789880.529161610101921.14405959072198
Trimmed Mean ( 5 / 24 )0.6386794720663050.5084893722434911.25603307941011
Trimmed Mean ( 6 / 24 )0.6731367051765370.4847890555864281.38851464862851
Trimmed Mean ( 7 / 24 )0.7012287038698430.4655872383630341.50611667608267
Trimmed Mean ( 8 / 24 )0.7170759456410330.4475469794348391.60223614188293
Trimmed Mean ( 9 / 24 )0.7272819541107570.4279931433988451.69928412482301
Trimmed Mean ( 10 / 24 )0.7493829890733620.4107854061908231.82426877337811
Trimmed Mean ( 11 / 24 )0.7679055027168840.3925525867347381.95618505307618
Trimmed Mean ( 12 / 24 )0.7749141374183350.3804830912270672.03665854090708
Trimmed Mean ( 13 / 24 )0.7827615954625180.3699096441467572.11608863907308
Trimmed Mean ( 14 / 24 )0.7814722902455530.3596106326402772.17310674188900
Trimmed Mean ( 15 / 24 )0.7859041089379630.3478553141447882.25928446966559
Trimmed Mean ( 16 / 24 )0.7840652173808670.3400676391931582.30561549238009
Trimmed Mean ( 17 / 24 )0.7781206844052670.3311994434060312.34940214996478
Trimmed Mean ( 18 / 24 )0.7715137213253230.3195738142595532.41419567843163
Trimmed Mean ( 19 / 24 )0.7753339766843150.3090401218114112.50884568689581
Trimmed Mean ( 20 / 24 )0.7922829788234570.3004839950580692.63668944720449
Trimmed Mean ( 21 / 24 )0.8012831092893110.2932191967965392.73271026605161
Trimmed Mean ( 22 / 24 )0.8102847813877150.2845064655520202.84803644028104
Trimmed Mean ( 23 / 24 )0.814008800437860.2763947473497392.94509504338679
Trimmed Mean ( 24 / 24 )0.8122696982816060.2656159195647673.05806105150841
Median0.445213929707559
Midrange1.1550915521331
Midmean - Weighted Average at Xnp0.680465897407428
Midmean - Weighted Average at X(n+1)p0.771513721325323
Midmean - Empirical Distribution Function0.771513721325323
Midmean - Empirical Distribution Function - Averaging0.771513721325323
Midmean - Empirical Distribution Function - Interpolation0.771513721325323
Midmean - Closest Observation0.679113380239706
Midmean - True Basic - Statistics Graphics Toolkit0.771513721325323
Midmean - MS Excel (old versions)0.771513721325323
Number of observations73
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196469974xltr73myfjjc060/1mtio1196470636.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196469974xltr73myfjjc060/1mtio1196470636.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196469974xltr73myfjjc060/23xua1196470636.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196469974xltr73myfjjc060/23xua1196470636.ps (open in new window)


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

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

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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