# This figure shows empirical CDFs for a small and a large sample # from the gamma distribution to demonstrate their convergence to # the empirical CDF. # # Figure caption: Convergence of the empirical cdf to the # theoretical cdf. The left panel displays the empirical cdf for # a random sample of size 10 from the gamma distribution whose pdf # is the top right band panel of figure 3.3, together with the # gamma cdf. The right panel shows the empirical cdf for a random # sample of size 200, again with the gamma cdf. In the right # panel, the empirical cdf is quite close to the theoretical gamma # cdf. # Set graphical parameters postscript("ecdf.ps") par(cex.lab=2) par(cex.axis=1.75) par(las=1) par(mfrow=c(1,2)) par(mar = c(4, 4, 1, 1)) # Generate data for samples of sizes 10 and 200. smallSample = rgamma(10, 2) largeSample = rgamma(200, 2) # Plot the smaller sample's empirical CDF, and add a line for the # theoretical CDF. xvals = sort(smallSample) yvals = (0:10)/10 fhat = stepfun(xvals, yvals, right = TRUE) plot(fhat, xlab = "", ylab = "", main = "", pch = 16, cex = 1) xseq = seq(-1, 12, length = 300) lines(xseq, pgamma(xseq, 2), lty = 5, lwd = 2, col = 4) # Do the same for the larger sample. xvals = sort(largeSample) yvals = (0:200)/200 fhat = stepfun(xvals, yvals, right = TRUE) plot(fhat, xlab = "", ylab = "", main = "", pch = 16, cex = 0.7) xseq = seq(-1, 12, length = 300) lines(xseq, pgamma(xseq, 2), lty = 5, lwd = 2, col = 4) # Close the graphics device. dev.off() #try library(Hmisc); use ecdf