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Data:
1.72923686058208 0.122433126801145 0.523768788982079 -0.50175942601324 -1.86386120887019 0.0717422351702872 -0.380578531491989 -0.29851611788274 1.94316215667028 -1.24779901378139 1.35257277275093 2.84406850014719 1.12274878943606 -2.32540657982629 -2.89902363942181 0.246874012745119 -0.731094375584061 1.97769407549524 -0.089308186457892 -1.64931358279907 1.78988776616251 -0.655026882699021 -0.95518008982139 -0.501427837065876 -1.47468882156665 2.4255103110643 -0.388732570521789 -1.41970373897772 -0.435743764210552 0.588337253253952 -1.73087780677345 0.416192838768035 -0.135602934239543 1.5607508968729 -0.619488852927662 0.130061173484127 -0.485714783249833 1.19042117073251 0.504940688912012 -0.266725732456376 1.8987616014054 0.9835731579105 0.221023228988728 -0.176860990484583 -0.162198287814433 0.78911590880292 1.41209201053576 0.518161844628975 2.36462043434148 -1.24446105804486 1.09138861156198 0.422175612267996 -0.997989397904933 0.754650745534752 -1.44375392644115 0.568632265545353 1.35413305240232 -1.34288885715882 -0.0968579661829751 0.242767533935212 0.255744783559028 -0.243232899636027 0.461607264600104 0.0650797112167817 2.25999343044582 1.80462197944889 2.32548979115297 0.682758803307819 -0.335554613197298 -0.997929583796738 0.97507128242145 -1.17268516900173 -0.000337278483281606 -1.71460596672184 -1.34872342854985 -1.6521456119588 -1.48335049731373 0.925016701443022 -0.226525557050897 0.774905929042345 -0.339789522342372 0.89311055438168 -0.864578780222597 -1.95217915873499 -0.11317194501752 1.02470860347022 -1.25650654087286 -0.602130638597027 -0.83233134657693 -0.446577198612737 -4.01053303468812 0.288513333839785 -1.00798474916531 -0.572816189634855 -0.297410570159231 1.21578539483534 -0.727486991378146 -0.843943364912431 -1.20889338911855 -0.649656515850742 3.19984732249364 0.572738529480399 -0.0199646221520179 0.462316869083462 -1.28699501625665 -1.80757939159691 -2.15431670426712 0.707840316820782 1.36410372036211 0.314718394752158 -4.1002515835693 1.26992188862053 1.80144339707427 -0.42970220964945 0.529993653035631 1.18764422512472 -0.398233352310507 -0.421884162222733 -2.6898323919027 1.0140628812162 -0.542058945797581 -0.368690243263354 1.31411524584048 -0.428705333764204 -0.663582558495647 1.37204511801761 -1.27310996987184 0.810157913937622 1.5741305304336 -1.025150115941 -0.998930862337702 -0.0536208441845616 1.66337771592794 -0.178008462116163 -1.09164775518912 1.96797905166753 0.634220496887586 1.38764487483822 0.75570654001001 -2.3214750727902 1.62023993830839 0.423224828517651 -1.7051130142733 0.541981863740972 -0.593027838089475 0.213567450337977 -0.696840242545287 0.0777251570183703 -0.725328497765991 2.1315776363419 -0.33645518676905 -0.979182554450992 -0.242246084610725 -1.82980075345691 -1.14814874978528 0.496126806273696 -0.37803015357093 0.564631359789787 0.268965939275992 0.752661368724124 -2.30203173253409 2.82635859577673 -0.607627712639158 3.77405193258893 1.08426693162876 -2.2508985634727 0.290663952981133 -1.1346060583543 1.41583984485642 0.590041695581542 1.22056539827692 0.0970995178245223 -0.906020145960084 -0.597681226735446 0.437155726246844 0.742487563055592 1.22917286536281 -0.95259160353182 -0.75528682870179
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R Code
library(car) load(file='createtable') hyperlink <- function(url,anchor,title,target=''){ anchor } x <-sort(x[!is.na(x)]) num <- 50 res <- array(NA,dim=c(num,3)) 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] } } } } iqd <- 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) } iqdiff <- qvalue3 - qvalue1 return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1))) } 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) } range <- max(x) - min(x) lx <- length(x) biasf <- (lx-1)/lx varx <- var(x) bvarx <- varx*biasf sdx <- sqrt(varx) mx <- mean(x) bsdx <- sqrt(bvarx) x2 <- x*x mse0 <- sum(x2)/lx xmm <- x-mx xmm2 <- xmm*xmm msem <- sum(xmm2)/lx axmm <- abs(x - mx) medx <- median(x) axmmed <- abs(x - medx) xmmed <- x - medx xmmed2 <- xmmed*xmmed msemed <- sum(xmmed2)/lx qarr <- array(NA,dim=c(8,3)) for (j in 1:8) { qarr[j,] <- iqd(x,j) } sdpo <- 0 adpo <- 0 for (i in 1:(lx-1)) { for (j in (i+1):lx) { ldi <- x[i]-x[j] aldi <- abs(ldi) sdpo = sdpo + ldi * ldi adpo = adpo + aldi } } denom <- (lx*(lx-1)/2) sdpo = sdpo / denom adpo = adpo / denom gmd <- 0 for (i in 1:lx) { for (j in 1:lx) { ldi <- abs(x[i]-x[j]) gmd = gmd + ldi } } gmd <- gmd / (lx*(lx-1)) sumx <- sum(x) pk <- x / sumx ck <- cumsum(pk) dk <- array(NA,dim=lx) for (i in 1:lx) { if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i] } bigd <- sum(dk) * 2 / (lx-1) iod <- 1 - sum(pk*pk) res[1,] <- c('Absolute range','http://www.xycoon.com/absolute.htm', signif(range,6)) res[2,] <- c('Relative range (unbiased)','http://www.xycoon.com/relative.htm', signif(range/sd(x),6)) res[3,] <- c('Relative range (biased)','http://www.xycoon.com/relative.htm', signif(range/sqrt(varx*biasf),6)) res[4,] <- c('Variance (unbiased)','http://www.xycoon.com/unbiased.htm', signif(varx,6)) res[5,] <- c('Variance (biased)','http://www.xycoon.com/biased.htm', signif(bvarx,6)) res[6,] <- c('Standard Deviation (unbiased)','http://www.xycoon.com/unbiased1.htm', signif(sdx,6)) res[7,] <- c('Standard Deviation (biased)','http://www.xycoon.com/biased1.htm', signif(bsdx,6)) res[8,] <- c('Coefficient of Variation (unbiased)','http://www.xycoon.com/variation.htm', signif(sdx/mx,6)) res[9,] <- c('Coefficient of Variation (biased)','http://www.xycoon.com/variation.htm', signif(bsdx/mx,6)) res[10,] <- c('Mean Squared Error (MSE versus 0)','http://www.xycoon.com/mse.htm', signif(mse0,6)) res[11,] <- c('Mean Squared Error (MSE versus Mean)','http://www.xycoon.com/mse.htm', signif(msem,6)) res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'http://www.xycoon.com/mean2.htm', signif(sum(axmm)/lx,6)) res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'http://www.xycoon.com/median1.htm', signif(sum(axmmed)/lx,6)) res[14,] <- c('Median Absolute Deviation from Mean', 'http://www.xycoon.com/mean3.htm', signif(median(axmm),6)) res[15,] <- c('Median Absolute Deviation from Median', 'http://www.xycoon.com/median2.htm', signif(median(axmmed),6)) res[16,] <- c('Mean Squared Deviation from Mean', 'http://www.xycoon.com/mean1.htm', signif(msem,6)) res[17,] <- c('Mean Squared Deviation from Median', 'http://www.xycoon.com/median.htm', signif(msemed,6)) mylink1 <- hyperlink('http://www.xycoon.com/difference.htm','Interquartile Difference','') mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ') res[18,] <- c('', mylink2, signif(qarr[1,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ') res[19,] <- c('', mylink2, signif(qarr[2,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ') res[20,] <- c('', mylink2, signif(qarr[3,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ') res[21,] <- c('', mylink2, signif(qarr[4,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ') res[22,] <- c('', mylink2, signif(qarr[5,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ') res[23,] <- c('', mylink2, signif(qarr[6,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ') res[24,] <- c('', mylink2, signif(qarr[7,1],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ') res[25,] <- c('', mylink2, signif(qarr[8,1],6)) mylink1 <- hyperlink('http://www.xycoon.com/deviation.htm','Semi Interquartile Difference','') mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ') res[26,] <- c('', mylink2, signif(qarr[1,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ') res[27,] <- c('', mylink2, signif(qarr[2,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ') res[28,] <- c('', mylink2, signif(qarr[3,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ') res[29,] <- c('', mylink2, signif(qarr[4,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ') res[30,] <- c('', mylink2, signif(qarr[5,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ') res[31,] <- c('', mylink2, signif(qarr[6,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ') res[32,] <- c('', mylink2, signif(qarr[7,2],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ') res[33,] <- c('', mylink2, signif(qarr[8,2],6)) mylink1 <- hyperlink('http://www.xycoon.com/variation1.htm','Coefficient of Quartile Variation','') mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ') res[34,] <- c('', mylink2, signif(qarr[1,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ') res[35,] <- c('', mylink2, signif(qarr[2,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ') res[36,] <- c('', mylink2, signif(qarr[3,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ') res[37,] <- c('', mylink2, signif(qarr[4,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ') res[38,] <- c('', mylink2, signif(qarr[5,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ') res[39,] <- c('', mylink2, signif(qarr[6,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ') res[40,] <- c('', mylink2, signif(qarr[7,3],6)) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ') res[41,] <- c('', mylink2, signif(qarr[8,3],6)) res[42,] <- c('Number of all Pairs of Observations', 'http://www.xycoon.com/pair_numbers.htm', signif(lx*(lx-1)/2,6)) res[43,] <- c('Squared Differences between all Pairs of Observations', 'http://www.xycoon.com/squared_differences.htm', signif(sdpo,6)) res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'http://www.xycoon.com/mean_abs_differences.htm', signif(adpo,6)) res[45,] <- c('Gini Mean Difference', 'http://www.xycoon.com/gini_mean_difference.htm', signif(gmd,6)) res[46,] <- c('Leik Measure of Dispersion', 'http://www.xycoon.com/leiks_d.htm', signif(bigd,6)) res[47,] <- c('Index of Diversity', 'http://www.xycoon.com/diversity.htm', signif(iod,6)) res[48,] <- c('Index of Qualitative Variation', 'http://www.xycoon.com/qualitative_variation.htm', signif(iod*lx/(lx-1),6)) res[49,] <- c('Coefficient of Dispersion', 'http://www.xycoon.com/dispersion.htm', signif(sum(axmm)/lx/medx,6)) res[50,] <- c('Observations', '', lx) print(res) (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) print(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='Robustness of Central Tendency', xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main='Robustness of Central Tendency', 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='Robustness of Central Tendency', xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main='Robustness of Central Tendency', xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() 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,signif(arm,6)) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', signif(armse,6), 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,signif(armose,6)) 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,signif(geo,6)) 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,signif(har,6)) 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,signif(qua,6)) 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,signif(win[j,1],6)) a<-table.element(a,signif(win[j,2],6)) a<-table.element(a,signif(win[j,1]/win[j,2],6)) 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,signif(tri[j,1],6)) a<-table.element(a,signif(tri[j,2],6)) a<-table.element(a,signif(tri[j,1]/tri[j,2],6)) 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,signif(median(x),6)) 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,signif(midr,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_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[1],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_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[2],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_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[3],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_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[4],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_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[5],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_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[6],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,signif(midm[7],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_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[8],6)) 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') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Variability - Ungrouped Data',2,TRUE) a<-table.row.end(a) for (i in 1:num) { a<-table.row.start(a) if (res[i,1] != '') { a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE) } else { a<-table.element(a,res[i,2],header=TRUE) } a<-table.element(a,res[i,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') lx <- length(x) qval <- array(NA,dim=c(99,8)) mystep <- 25 mystart <- 25 if (lx>10){ mystep=10 mystart=10 } if (lx>20){ mystep=5 mystart=5 } if (lx>50){ mystep=2 mystart=2 } if (lx>=100){ mystep=1 mystart=1 } for (perc in seq(mystart,99,mystep)) { qval[perc,1] <- q1(x,lx,perc/100,i,f) qval[perc,2] <- q2(x,lx,perc/100,i,f) qval[perc,3] <- q3(x,lx,perc/100,i,f) qval[perc,4] <- q4(x,lx,perc/100,i,f) qval[perc,5] <- q5(x,lx,perc/100,i,f) qval[perc,6] <- q6(x,lx,perc/100,i,f) qval[perc,7] <- q7(x,lx,perc/100,i,f) qval[perc,8] <- q8(x,lx,perc/100,i,f) } bitmap(file='test3.png') qqPlot(x,dist='norm',main='QQ plot (Normal) with confidence intervals') grid() dev.off() a<-table.start() a<-table.row.start(a) a<-table.element(a,'Percentiles - Ungrouped Data',9,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p',1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_1.htm', 'Weighted Average at Xnp',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),1,TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),1,TRUE) a<-table.row.end(a) for (perc in seq(mystart,99,mystep)) { a<-table.row.start(a) a<-table.element(a,round(perc/100,2),1,TRUE) for (j in 1:8) { a<-table.element(a,round(qval[perc,j],6)) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') bitmap(file='histogram1.png') myhist<-hist(x) dev.off() myhist n <- length(x) a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/histogram.htm','Frequency Table (Histogram)',''),6,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Bins',header=TRUE) a<-table.element(a,'Midpoint',header=TRUE) a<-table.element(a,'Abs. Frequency',header=TRUE) a<-table.element(a,'Rel. Frequency',header=TRUE) a<-table.element(a,'Cumul. Rel. Freq.',header=TRUE) a<-table.element(a,'Density',header=TRUE) a<-table.row.end(a) crf <- 0 mybracket <- '[' mynumrows <- (length(myhist$breaks)-1) for (i in 1:mynumrows) { a<-table.row.start(a) if (i == 1) dum <- paste('[',myhist$breaks[i],sep='') else dum <- paste(mybracket,myhist$breaks[i],sep='') dum <- paste(dum,myhist$breaks[i+1],sep=',') if (i==mynumrows) dum <- paste(dum,']',sep='') else dum <- paste(dum,mybracket,sep='') a<-table.element(a,dum,header=TRUE) a<-table.element(a,myhist$mids[i]) a<-table.element(a,myhist$counts[i]) rf <- myhist$counts[i]/n crf <- crf + rf a<-table.element(a,round(rf,6)) a<-table.element(a,round(crf,6)) a<-table.element(a,round(myhist$density[i],6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') bitmap(file='density1.png') mydensity1<-density(x,kernel='gaussian',na.rm=TRUE) plot(mydensity1,main='Gaussian Kernel') grid() dev.off() mydensity1 a<-table.start() a<-table.row.start(a) a<-table.element(a,'Properties of Density Trace',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Bandwidth',header=TRUE) a<-table.element(a,mydensity1$bw) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'#Observations',header=TRUE) a<-table.element(a,mydensity1$n) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable4.tab')
Compute
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Raw Input
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Raw Output
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Computing time
1 seconds
R Server
Big Analytics Cloud Computing Center
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