EXPECTED VALUES OF EXPONENTIAL, WEIBULL AND GAMMA ORDER STATISTICS

摘要

Five-decimal-place tables, accurate to within a unit in the last place, are given of the expected values of the M order statistics [ M= 1 (1)N] of samples of size N from the exponential population [N = 1 (1) 120] and from the Weibull and Gamma populations [N = 1 (1)40]. In each case, the values of the location and scale parameters are assumed to be 0 and I, respectively. Results are tabulated for the Weibull population with shape parameter K = 0. 5(0. 5)4(1)8 and for the Gamma population with shape parameter a - 0. 5(0. 5)4, as well as for the exponential population, which is a special case, (shape parameter 1 ) of each of the other two populations. Also given is an eight-decimal-place table, accurate to within a unit in the last place, of the moments (mean, variance, skewness, and kurtosis) of the exponential population and of the Weibull and Gamma populations with the above-mentioned values of the shape parameters. The mathematical formulations are given, along with a description of the methods of computation and a discussion of uses of the tables.