1/24/2006 12:23:00 AM   2006-01-24 Uniform Distributions The uniform distributions (continuous) are probability distributions such that all intervals of the same length are equally probable. Uses of the uniform distribution In statistics, when a p-value is used as a test statistic for a simple null hypothesis, and the distribution of the test statistic is continuous, then the test statistic is uniformly distributed between 0 and 1 if the null hypothesis is true. Although the uniform distribution is not commonly found in nature, it is particularly useful for sampling from arbitrary distributions.