Opgave 5, Oefening 2, Stap 1, Sara Vandenberghe

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 20 Mar 2009 17:35:14 -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/Mar/21/t1237592158v4wtbekerc5ufbz.htm/, Retrieved Sat, 21 Mar 2009 00:35:58 +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/2009/Mar/21/t1237592158v4wtbekerc5ufbz.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 «

1,54 1,55 1,53 1,55 1,55 1,53 1,54 1,54 1,54 1,53 1,53 1,53 1,54 1,53 1,53 1,54 1,55 1,53 1,53 1,53 1,53 1,52 1,54 1,53 1,52 1,54 1,53 1,54 1,54 1,53 1,54 1,54 1,52 1,52 1,57 1,6 1,59 1,6 1,6 1,62 1,61 1,61 1,62 1,61 1,62 1,61 1,62 1,61 1,61 1,58 1,57 1,57 1,66 1,66 1,67 1,68 1,66 1,66 1,64 1,61 1,58 1,57 1,54 1,61 1,65 1,6 1,57 1,56 1,55 1,54 1,51 1,5 1,5 1,49 1,47 1,47 1,49 1,49 1,49 1,51 1,49 1,48 1,46 1,46 1,45 1,45 1,44 1,47 1,47 1,45 1,43 1,44 1,38 1,4 1,37 1,41

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 1.54145833333333 0.00670653511912773 229.844219996244 Geometric Mean 1.54006269013659 Harmonic Mean 1.53865674591192 Quadratic Mean 1.54284369482675 Winsorized Mean ( 1 / 32 ) 1.54145833333333 0.00665730565373496 231.5438727781 Winsorized Mean ( 2 / 32 ) 1.54166666666667 0.00651527669476568 236.623360586547 Winsorized Mean ( 3 / 32 ) 1.54197916666667 0.00644582652898858 239.221325571202 Winsorized Mean ( 4 / 32 ) 1.5428125 0.00627705219989252 245.786151025862 Winsorized Mean ( 5 / 32 ) 1.54333333333333 0.0061819393614792 249.651968919353 Winsorized Mean ( 6 / 32 ) 1.54270833333333 0.00606159749416658 254.505241368792 Winsorized Mean ( 7 / 32 ) 1.54270833333333 0.00580282592731249 265.854663341214 Winsorized Mean ( 8 / 32 ) 1.54104166666667 0.00552998042306953 278.670365673968 Winsorized Mean ( 9 / 32 ) 1.54104166666667 0.00552998042306953 278.670365673968 Winsorized Mean ( 10 / 32 ) 1.54208333333333 0.00535559362171326 287.938824760946 Winsorized Mean ( 11 / 32 ) 1.54208333333333 0.00535559362171326 287.938824760946 Winsorized Mean ( 12 / 32 ) 1.54208333333333 0.00497343087012206 310.064294368183 Winsorized Mean ( 13 / 32 ) 1.54208333333333 0.00497343087012206 310.064294368183 Winsorized Mean ( 14 / 32 ) 1.54208333333333 0.00497343087012206 310.064294368183 Winsorized Mean ( 15 / 32 ) 1.54208333333333 0.00497343087012206 310.064294368183 Winsorized Mean ( 16 / 32 ) 1.54375 0.00472778739837258 326.526950118653 Winsorized Mean ( 17 / 32 ) 1.54552083333333 0.00448650459728529 344.482168650513 Winsorized Mean ( 18 / 32 ) 1.54552083333333 0.00448650459728529 344.482168650513 Winsorized Mean ( 19 / 32 ) 1.54552083333333 0.00448650459728529 344.482168650513 Winsorized Mean ( 20 / 32 ) 1.5434375 0.00418022738458593 369.223335958047 Winsorized Mean ( 21 / 32 ) 1.5434375 0.00418022738458593 369.223335958047 Winsorized Mean ( 22 / 32 ) 1.54572916666667 0.00388357085995209 398.017500493279 Winsorized Mean ( 23 / 32 ) 1.54572916666667 0.00388357085995209 398.017500493279 Winsorized Mean ( 24 / 32 ) 1.54572916666667 0.00321640801500771 480.576207823857 Winsorized Mean ( 25 / 32 ) 1.543125 0.0028497172066531 541.501099266039 Winsorized Mean ( 26 / 32 ) 1.54583333333333 0.00253772703014571 609.140902457336 Winsorized Mean ( 27 / 32 ) 1.54302083333333 0.00215170165048272 717.116535643855 Winsorized Mean ( 28 / 32 ) 1.54302083333333 0.00215170165048272 717.116535643855 Winsorized Mean ( 29 / 32 ) 1.54302083333333 0.00215170165048272 717.116535643855 Winsorized Mean ( 30 / 32 ) 1.54614583333333 0.00182796137806782 845.830689796974 Winsorized Mean ( 31 / 32 ) 1.54614583333333 0.00182796137806782 845.830689796974 Winsorized Mean ( 32 / 32 ) 1.5428125 0.00137890692948271 1118.86630418108 Trimmed Mean ( 1 / 32 ) 1.54180851063830 0.00643138247422725 239.732050895255 Trimmed Mean ( 2 / 32 ) 1.54217391304348 0.00617244250772292 249.848242590177 Trimmed Mean ( 3 / 32 ) 1.54244444444444 0.00596349927670397 258.647544482802 Trimmed Mean ( 4 / 32 ) 1.54261363636364 0.00575422773607419 268.083521737025 Trimmed Mean ( 5 / 32 ) 1.54255813953488 0.00557301011707534 276.790837829019 Trimmed Mean ( 6 / 32 ) 1.54238095238095 0.00539229558019438 286.034199988227 Trimmed Mean ( 7 / 32 ) 1.54231707317073 0.00521532376193645 295.72796312804 Trimmed Mean ( 8 / 32 ) 1.54225 0.00507218463406305 304.060303649591 Trimmed Mean ( 9 / 32 ) 1.54243589743590 0.0049646968721998 310.680780144481 Trimmed Mean ( 10 / 32 ) 1.54263157894737 0.00483905319524472 318.787894388781 Trimmed Mean ( 11 / 32 ) 1.54270270270270 0.00472610534427523 326.421564972391 Trimmed Mean ( 12 / 32 ) 1.54277777777778 0.00459307425074502 335.892191929519 Trimmed Mean ( 13 / 32 ) 1.54285714285714 0.00450508273865263 342.470323490346 Trimmed Mean ( 14 / 32 ) 1.54294117647059 0.00440018967350686 350.653333368899 Trimmed Mean ( 15 / 32 ) 1.54303030303030 0.00427476847868664 360.962309590244 Trimmed Mean ( 16 / 32 ) 1.543125 0.00412403788683658 374.17818224354 Trimmed Mean ( 17 / 32 ) 1.54306451612903 0.00398694796571286 387.029008002901 Trimmed Mean ( 18 / 32 ) 1.54283333333333 0.00386269765125481 399.418611713536 Trimmed Mean ( 19 / 32 ) 1.54258620689655 0.00371032424987041 415.755093897906 Trimmed Mean ( 20 / 32 ) 1.54232142857143 0.00352164984421108 437.954225093307 Trimmed Mean ( 21 / 32 ) 1.54222222222222 0.00335075809049817 460.260687453249 Trimmed Mean ( 22 / 32 ) 1.54211538461538 0.00313517169276301 491.875895720508 Trimmed Mean ( 23 / 32 ) 1.5418 0.00292337518101588 527.404080739381 Trimmed Mean ( 24 / 32 ) 1.54145833333333 0.00264624689625398 582.507375073512 Trimmed Mean ( 25 / 32 ) 1.54108695652174 0.00245201801676647 628.497403356768 Trimmed Mean ( 26 / 32 ) 1.54090909090909 0.00229481863797625 671.473146247403 Trimmed Mean ( 27 / 32 ) 1.54047619047619 0.00215411932718922 715.13038810448 Trimmed Mean ( 28 / 32 ) 1.54025 0.00207202056716849 743.35652087895 Trimmed Mean ( 29 / 32 ) 1.54 0.00195976600339204 785.808100219366 Trimmed Mean ( 30 / 32 ) 1.53972222222222 0.00180326472500028 853.85257132559 Trimmed Mean ( 31 / 32 ) 1.53911764705882 0.00165509245256217 929.928503193998 Trimmed Mean ( 32 / 32 ) 1.5384375 0.00142764857144480 1077.60238112596 Median 1.54 Midrange 1.525 Midmean - Weighted Average at Xnp 1.5398 Midmean - Weighted Average at X(n+1)p 1.54145833333333 Midmean - Empirical Distribution Function 1.5398 Midmean - Empirical Distribution Function - Averaging 1.54145833333333 Midmean - Empirical Distribution Function - Interpolation 1.54145833333333 Midmean - Closest Observation 1.5398 Midmean - True Basic - Statistics Graphics Toolkit 1.54145833333333 Midmean - MS Excel (old versions) 1.54425925925926 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/21/t1237592158v4wtbekerc5ufbz/1x03x1237592110.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/21/t1237592158v4wtbekerc5ufbz/1x03x1237592110.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/21/t1237592158v4wtbekerc5ufbz/2z1z41237592110.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/21/t1237592158v4wtbekerc5ufbz/2z1z41237592110.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')

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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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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