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Classical continuous goodness-of-fit (GOF) testing is employed for examining whether the data come from an assumed parametric model. In many cases, GOF tests assume a uniform null distribution and examine extreme values of the order statistics of the samples. Many of these statistics can be expressed by a function of the order statistics and the  p -values amount to a joint probability statement based on the uniform order statistics. In this paper, we utilize Steck's recursion method and propose two high precision computing algorithms to compute the  p -values for these GOF statistics. The numerical difficulties in implementing Steck's method are discussed and compared with solutions provided in high precision libraries.

High precision implementation of Steck's recursion method for use in goodness-of-fit tests