This chapter presents an omnibus test to test any distributional assumption. It is based on the regression test of Brain and Shapiro to test for an underlying exponential distribution. The chapter extends the results of Gulati and Shapiro and Gulati to develop a universal test for all single-parameter or two-parameter distributions based on the Brain and Shapiro test. The procedure proposed by Brain and Shapiro determines exponentiality of the given data by testing whether the underlying failure rate function is constant and is based on the fact that the ordered weighted spacings of i.i.d. exponential random variables are independent and identically distributed (i.i.d.) exponential. The Brain and Shapiro test is used to test for any underlying distribution. The chapter deals with simulation studies to assess the null distribution of the statistic and corresponding power studies for various distributions characterized by a scale parameter or a scale and a shape parameter.
