A Monte Carlo Technique Using Linear Interpolation to Generate Modified Kolmogorov-Smirnov Critical Values for the Extreme Value Distribution.

摘要

An investigation was conducted to examine the merits of an estimation technique involving linear interpolation to estimate Kolmogorov-Smirnov (K-S) critical values when the scale and location parameters of the hypothesized distribution are unknown. The purpose of the linear estimation technique is to reduce the number of Monte Carlo generated samples necessary to produce useful critical values for the K-S goodness-of-fit test. Also, different plotting positions were studied to ascertain which plotting positions used in calculating and plotting the K-S test statistic values provided the best critical value estimation. In addition, a power study was performed which compared the power of the true critical values against the power of the estimated critical values. Useful critical values were found with the linear estimation technique using relatively few Monte Carlo generated samples. Further, the plotting positions found to be the best in calculating the K-S text statistic values and plotting these values were respectively i/n and (i-.5)/n where i is the ith ranked point in a sample of size n.