| Abstract: | A Monte Carlo study was made of the effects of using simple linear regression, on the appropriate probability paper, to estimate parameters, quantiles and cumulative probability for several distributions. These distributions were the Normal, Weibull (shape parameters 1, 2, and 4) and the Type I largest extreme-value distributions. The specific objective was to observe differences arising from choice of plotting positions. Plotting positions used were i/(n+l), (i?3)/(n+.04), (i?.5)/n, either (i?.375)/(n+.25) or (i?.4)/(n+.2), and either F[E(Yi)] or F[E(£n Y)]. For each combination of 4 sample sizes (n=10(10)(40)), distribution, and plotting position, regression lines were found for each of N =9999 samples. Each regression line was used to estimate: (1) quantiles of 9 specific probabilities, (2) probabilities of 9 specific quantiles, and (3) return periods corresponding to 9 specific quantiles. Compa[rgrave]ison of the mean, variances, mean square error and medians of these estimates and of the regression coefficients confirm some results of Harter [Commun. Statist. A13(13), 1984] and provide further insight. |
