An Unbinned Goodness-of-Fit Test Based on the Random Walk

Abstract

We describe a test statistic for unbinned goodness-of-fit of data in one dimension. The statistic is based on the two-dimensional Random Walk. The rejection power of this test is explored both for simple and compound hypotheses and, for the examples explored, it is found to be comparable to that for the chisquare test. We discuss briefly how it may be possible to extend this test to multi-dimensional data.