Normal Characteristics of the Weibull Order Statistic Distribution.

This report developed a technique to measure how closely the Weibull order statistic distribution, for a certain range of its parameters, approximates a normal distribution. This technique used the analytical expressions for the mean and variance of the Weibull order statistic distribution to approximate the mean and variance of the normal distribution. Using these approximations, the standard normal deviates for the 75th, 90th, and 95th percentiles were compared with the actual values to ascertain whether the approximation is acceptable. The acceptance criteria used in this paper is to accept the approximation when each of the errors is less than 10.