A New Goodness-of-Fit Test for the Weibull Distribution Based on Spacings

The critical values for a new goodness-of-fit test based on spacings are generated for the Weibull distribution when the shape parameter is known. The critical values are used for testing whether a set of observations follow a Weibull distribution when the scale and location parameters are unknown. A Monte Carlo simulation with 10,000 iterations is used to generate the critical values for sample sizes 5(5)35 at shape parameters k equal to 0.5(0.5)1.5 and for sample sizes 5(5)20 at shape parameters k = 2.0(1.0)4.0. A Monte Carlo power study of the Z* test statistic using 5000 iterations is accomplished using nine alternate distributions H sub A. The power is good to excellent when the null hypothesis Ho is from a skewed distribution(k < 2.0). Power results at shape parameters k > 2.0 are poor for all sample sizes considered. A comparison is made, at shape parameter 1.0, against the prominent competing goodness-of-fit test statistics. Data is obtained from a prior AFIT thesis by Bush. Results indicate that the Z* test is more powerful than the competition at the available sample sizes of 5, 15 and 25 and alpha levels: 0.05 and 0.01. A relationship between the critical value and the sample size is investigated to allow for greater usage of the test statistic. Satisfactory values of fit are attained with a simple log-linear relationship.... Goodness-of-Fit Test, Weibull Distribution, Spacings.