Survey of Properties and Applications of the Noncentral<i>t</i>-Distribution

Abstract

Applications are outlined of the noncentral t-distribution to tolerance limits, to variables sampling plans, to confidence limits on a quantile, to confidence limits on a proportion, to the distribution of the sample coefficient of variation, and to the power of Student's t-test. The basic assumption is that there is available a random sample from a normal distribution with mean and variance unknown. Some of the mathematical properties of the noncentral t-distribution are also outlined. An extensive bibliography has been prepared and cross-referenced to several review journals and books. The bibliography covers references to tolerance limits and sampling plans based on the normal distribution whether or not the noncentral t-distribution is directly involved. Some selected references to Student's t-distribution are also included.