::Free Statistics and Forecasting Software::

v1.2.1

:: Blocked Bootstrap Plot - Central Tendency - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Blocked Bootstrap Plot for three measures of Central Tendency: mean, median, and midrange. This method can be applied to univariate, stationary time series.
The following charts are generated by this module: sequences of simulated values (mean, median, and midrange), density trace of each eastimation, and notched boxplots of simulated values.
The blocked bootstrap simulation algorithm is used with a fixed (user-defined) window (blockwidth).

For more information about the bootstrap: Davison, A.C. and Hinkley, D.V. (1997), Bootstrap Methods and Their Application,. Cambridge University Press.

Enter (or paste) your data delimited by hard returns.

 Send output to: Browser Blue - Charts White Browser Black/White CSV Data[reset data] 3.11588143740481 0.556326671130017 0.792793547335559 0.753540227041097 -1.06256050719981 0.554932920759569 -0.471813339871471 0.724190368324084 2.34875358238066 -1.44100350845616 1.70011392810686 2.67190769477753 1.68394591488614 -2.01917739379323 -3.66229350458446 0.0140835434638608 -0.878462574457164 3.53631380169706 0.60736808655032 -1.309070568933 1.36445275604658 0.575098282436716 -0.120050376918307 0.0140835434638608 -1.95504040279298 1.82652332414746 0.306896664000228 -0.448728032797734 1.21561079514198 1.68035118365668 -2.98737642923443 0.604764488464347 0.414284323751355 1.10822313539085 0.620866279357225 -0.915853304826368 -0.232492740597185 1.19804903155081 0.00204532335525059 -0.564492959100168 2.09066137179968 0.155200980026887 2.40509982671149 -0.145586789833823 0.321538482194811 2.14170278721998 1.85466333514895 0.992860826315384 3.32153848219481 -0.844799019973113 1.56591378539685 0.0933311922134991 -1.01958001102019 1.35526825900671 -1.4017501881617 0.544288451021407 1.98879725553112 -2.97753918998483 -0.568153912657471 0.165779227437202 -1.07859607576484 0.217070767840275 1.53923374709366 -0.556115692548861 3.36730647911532 2.46917059538388 2.9122194271953 1.27869043067089 0.726793966410057 -0.682525088589457 0.130655700254855 -1.55757566524716 -0.206803835437475 -2.12517130317391 -1.95730760597984 -2.40442000857552 -3.00161563020205 0.869305153343531 0.133509423323598 0.240897083074725 -1.40733995397211 1.4207990003774 -0.0650978829579298 -1.21679356693127 0.603304515766052 0.5982498118383 -0.896831568536899 -0.316054085113862 0.11740763243072 0.240897083074725 -3.089240545503 1.69499300185126 -0.644665518665442 0.387538063120315 0.669237874363708 1.15374100732859 0.216754420529656 -0.478328016497518 -2.3105305416313 -0.646191713691585 2.12147120321499 1.72679396641006 0.554932920759569 0.316014938712248 -2.93608488883136 -1.07859607576484 -2.57659740153663 0.0035052960535461 0.742961979630783 0.717675691698037 -4.77666468051645 1.03310527975333 1.27822159111608 0.621335118912038 0.842625115040338 2.15374100732859 0.441030584382396 -0.430425261045848 -3.20987627307826 1.28015040336919 -0.346863916529171 0.74435573000123 2.19944278192125 0.122931175913283 -0.792832693737175 0.18188101833008 -1.01958001102019 0.0851378283171158 1.64255783606051 -3.38971196805309 -1.19662820525413 -0.310530541631299 0.707031221959875 0.608828059248615 -3.44872803279773 0.879949623081693 -0.53873783161261 0.555335537986534 1.33218295193297 -3.43554618730145 0.851809612080205 -1.09835882021502 -2.92690039179149 0.0224608100151677 -1.21639094970431 0.884013193865961 -1.89323683730744 0.273166887188329 -1.95510662512083 2.2907286507795 -0.569613885355767 -1.44466446201347 -0.650255284475853 -2.4406008912292 -0.224768216255613 1.23031883566441 -0.342800345744903 -1.24214607719186 -0.0877805728047026 1.00083547563973 -2.41791820138243 1.53371020361109 -0.391105718423537 1.42340259846337 0.536313801697065 -1.67700154510689 -1.01818626064974 -1.0841196192474 0.898721234388392 0.360791802489274 0.67988234410187 0.446554127864959 -1.26907624047783 -0.130628624328621 -0.772601109732181 0.910759454497002 1.61388276317637 -2.36442568012034 -1.4542515762803 # simulations blockwidth of bootstrap Significant digits Quantiles P1 P5 Q1 Q3 P95 P99P0.5 P2.5 Q1 Q3 P97.5 P99.5P10 P20 Q1 Q3 P80 P90 bandwidth Chart options Width: Height:

 Source code of R module par1 <- as.numeric(par1) par2 <- as.numeric(par2) par3 <- as.numeric(par3) if (par1 < 10) par1 = 10 if (par1 > 5000) par1 = 5000 if (par2 < 3) par2 = 3 if (par2 > length(x)) par2 = length(x) bw <- as.numeric(par5) if(bw < 0) bw=0.1 library(modeest) library(lattice) library(boot) boot.stat <- function(s) { s.mean <- mean(s) s.median <- median(s) s.midrange <- (max(s) + min(s)) / 2 s.mode <- hrm(s, bw=bw) s.kernelmode <- mlv(s, method="parzen", kernel="gaussian") c(s.mean, s.median, s.midrange, s.mode, s.kernelmode) } (r <- tsboot(x, boot.stat, R=par1, l=12, sim="fixed")) bitmap(file="plot1.png") plot(r\$t[,1],type="p",ylab="simulated values",main="Simulation of Mean") grid() dev.off() bitmap(file="plot2.png") plot(r\$t[,2],type="p",ylab="simulated values",main="Simulation of Median") grid() dev.off() bitmap(file="plot3.png") plot(r\$t[,3],type="p",ylab="simulated values",main="Simulation of Midrange") grid() dev.off() bitmap(file="plot7a.png") plot(r\$t[,4],type="p",ylab="simulated values",main="Simulation of Mode") grid() dev.off() bitmap(file="plot8a.png") plot(r\$t[,5],type="p",ylab="simulated values",main="Simulation of Mode of Kernel Density") grid() dev.off() bitmap(file="plot4.png") densityplot(~r\$t[,1],col="black",main="Density Plot",xlab="mean") dev.off() bitmap(file="plot5.png") densityplot(~r\$t[,2],col="black",main="Density Plot",xlab="median") dev.off() bitmap(file="plot6.png") densityplot(~r\$t[,3],col="black",main="Density Plot",xlab="midrange") dev.off() z <- data.frame(cbind(r\$t[,1],r\$t[,2],r\$t[,3],r\$t[,4],r\$t[,5]) ) colnames(z) <- list("mean","median","midrange","mode","mode.k.dens") bitmap(file="plot7.png") boxplot(z,notch=TRUE,ylab="simulated values",main="Bootstrap Simulation - Central Tendency") grid() dev.off() if (par4 == "P1 P5 Q1 Q3 P95 P99") { myq.1 <- 0.01 myq.2 <- 0.05 myq.3 <- 0.95 myq.4 <- 0.99 myl.1 <- "P1" myl.2 <- "P5" myl.3 <- "P95" myl.4 <- "P99" } if (par4 == "P0.5 P2.5 Q1 Q3 P97.5 P99.5") { myq.1 <- 0.005 myq.2 <- 0.025 myq.3 <- 0.975 myq.4 <- 0.995 myl.1 <- "P0.5" myl.2 <- "P2.5" myl.3 <- "P97.5" myl.4 <- "P99.5" } if (par4 == "P10 P20 Q1 Q3 P80 P90") { myq.1 <- 0.10 myq.2 <- 0.20 myq.3 <- 0.80 myq.4 <- 0.90 myl.1 <- "P10" myl.2 <- "P20" myl.3 <- "P80" myl.4 <- "P90" } load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Estimation Results of Blocked Bootstrap",10,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"statistic",header=TRUE) a<-table.element(a,myl.1,header=TRUE) a<-table.element(a,myl.2,header=TRUE) a<-table.element(a,"Q1",header=TRUE) a<-table.element(a,"Estimate",header=TRUE) a<-table.element(a,"Q3",header=TRUE) a<-table.element(a,myl.3,header=TRUE) a<-table.element(a,myl.4,header=TRUE) a<-table.element(a,"S.D.",header=TRUE) a<-table.element(a,"IQR",header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mean",header=TRUE) q1 <- quantile(r\$t[,1],0.25)[[1]] q3 <- quantile(r\$t[,1],0.75)[[1]] p01 <- quantile(r\$t[,1],myq.1)[[1]] p05 <- quantile(r\$t[,1],myq.2)[[1]] p95 <- quantile(r\$t[,1],myq.3)[[1]] p99 <- quantile(r\$t[,1],myq.4)[[1]] a<-table.element(a,signif(p01,par3)) a<-table.element(a,signif(p05,par3)) a<-table.element(a,signif(q1,par3)) a<-table.element(a,signif(r\$t0[1],par3)) a<-table.element(a,signif(q3,par3)) a<-table.element(a,signif(p95,par3)) a<-table.element(a,signif(p99,par3)) a<-table.element( a,signif( sqrt(var(r\$t[,1])),par3 ) ) a<-table.element(a,signif(q3-q1,par3)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"median",header=TRUE) q1 <- quantile(r\$t[,2],0.25)[[1]] q3 <- quantile(r\$t[,2],0.75)[[1]] p01 <- quantile(r\$t[,2],myq.1)[[1]] p05 <- quantile(r\$t[,2],myq.2)[[1]] p95 <- quantile(r\$t[,2],myq.3)[[1]] p99 <- quantile(r\$t[,2],myq.4)[[1]] a<-table.element(a,signif(p01,par3)) a<-table.element(a,signif(p05,par3)) a<-table.element(a,signif(q1,par3)) a<-table.element(a,signif(r\$t0[2],par3)) a<-table.element(a,signif(q3,par3)) a<-table.element(a,signif(p95,par3)) a<-table.element(a,signif(p99,par3)) a<-table.element(a,signif(sqrt(var(r\$t[,2])),par3)) a<-table.element(a,signif(q3-q1,par3)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"midrange",header=TRUE) q1 <- quantile(r\$t[,3],0.25)[[1]] q3 <- quantile(r\$t[,3],0.75)[[1]] p01 <- quantile(r\$t[,3],myq.1)[[1]] p05 <- quantile(r\$t[,3],myq.2)[[1]] p95 <- quantile(r\$t[,3],myq.3)[[1]] p99 <- quantile(r\$t[,3],myq.4)[[1]] a<-table.element(a,signif(p01,par3)) a<-table.element(a,signif(p05,par3)) a<-table.element(a,signif(q1,par3)) a<-table.element(a,signif(r\$t0[3],par3)) a<-table.element(a,signif(q3,par3)) a<-table.element(a,signif(p95,par3)) a<-table.element(a,signif(p99,par3)) a<-table.element(a,signif(sqrt(var(r\$t[,3])),par3)) a<-table.element(a,signif(q3-q1,par3)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mode",header=TRUE) q1 <- quantile(r\$t[,4],0.25)[[1]] q3 <- quantile(r\$t[,4],0.75)[[1]] p01 <- quantile(r\$t[,4],myq.1)[[1]] p05 <- quantile(r\$t[,4],myq.2)[[1]] p95 <- quantile(r\$t[,4],myq.3)[[1]] p99 <- quantile(r\$t[,4],myq.4)[[1]] a<-table.element(a,signif(p01,par3)) a<-table.element(a,signif(p05,par3)) a<-table.element(a,signif(q1,par3)) a<-table.element(a,signif(r\$t0[4],par3)) a<-table.element(a,signif(q3,par3)) a<-table.element(a,signif(p95,par3)) a<-table.element(a,signif(p99,par3)) a<-table.element(a,signif(sqrt(var(r\$t[,4])),par3)) a<-table.element(a,signif(q3-q1,par3)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mode k.dens",header=TRUE) q1 <- quantile(r\$t[,5],0.25)[[1]] q3 <- quantile(r\$t[,5],0.75)[[1]] p01 <- quantile(r\$t[,5],myq.1)[[1]] p05 <- quantile(r\$t[,5],myq.2)[[1]] p95 <- quantile(r\$t[,5],myq.3)[[1]] p99 <- quantile(r\$t[,5],myq.4)[[1]] a<-table.element(a,signif(p01,par3)) a<-table.element(a,signif(p05,par3)) a<-table.element(a,signif(q1,par3)) a<-table.element(a,signif(r\$t0[5],par3)) a<-table.element(a,signif(q3,par3)) a<-table.element(a,signif(p95,par3)) a<-table.element(a,signif(p99,par3)) a<-table.element(a,signif(sqrt(var(r\$t[,5])),par3)) a<-table.element(a,signif(q3-q1,par3)) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")
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 Cite this software as: Wessa P., (2019), Blocked Bootstrap Plot for Central Tendency (v1.0.7) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_bootstrapplot.wasp/ The R code is based on : Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988), The New S Language, Wadsworth & Brooks/Cole. Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A., (1983), Graphical Methods for Data Analysis., Wadsworth & Brooks/Cole. Murrell, P. (2005), R Graphics, Chapman & Hall/CRC Press. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03. Scott, D. W. (1992), Multivariate Density Estimation. Theory, Practice and Visualization, New York: Wiley. Sheather, S. J. and Jones M. C. (1991), A reliable data-based bandwidth selection method for kernel density estimation., J. Roy. Statist. Soc. B, 683-690. Silverman, B. W. (1986), Density Estimation, London: Chapman and Hall. Venables, W. N. and Ripley, B. D. (2002), Modern Applied Statistics with S, New York: Springer. S original by Angelo Canty R port by Brian Ripley, boot: Bootstrap R (S-Plus) Functions (Canty), 2005
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 To cite Wessa.net in publications use:Wessa, P. (2021), Free Statistics Software, Office for Research Development and Education, version 1.2.1, URL https://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. 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. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes 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. Software Version : 1.2.1Algorithms & Software : Patrick Wessa, PhDServer : supernova.wessa.net