Exponentiality Test Procedures for Large Samples of Rainfall Event Characteristics

Abstract

The main purpose of this paper is to examine and recommend procedures that can be used to statistically test the exponentiality of large amounts of sample data for rainfall event volume, duration, and interevent time. Based on literature review and initial analysis, the Poisson and chi-square goodness-of-fit tests are selected first. Some misconceptions about parameter estimators and degrees of freedom associated with the use of the chi-square goodness-of-fit tests are then clarified. Using rainfall data from seven stations in the north-central region of the United States, the choice of the event volume threshold and the minimum interevent time for separating continuous rainfall data into individual events are examined in detail. Findings from this study suggest that the Poisson test can be used for testing the exponentiality of interevent times and for examining the statistical independence of consecutive rainfall events. The use of the minimum chi-square estimator combined with the chi-square goodness-of-fit test is recommended for rainfall event volume and duration. An equation that can be used to determine the appropriate number of bins for grouping sample data when conducting the chi-square goodness-of-fit tests is also proposed.