::Free Statistics and Forecasting Software::

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.

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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")

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

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Algorithms & Software : Patrick Wessa, PhD
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