Comparison of the Power of Lognormality Tests with Different Right-Tail Alternative Distributions

Abstract

In flood frequency analysis (FFA), the adequate choice of distribution to fit data is a major problem. The three-parameter lognormal (LN3) distribution has an intermediate tail behavior between the distributions of the Class C (regularly varying distributions) and those of the Class D (subexponential distributions). HYFRAN software performs a complete frequency analysis for approximately twenty distributions often used in hydrology including the LN3 and distributions of Classes C and D. A decision support system (DSS) was added to the HYFRAN software to become the HYFRAN-PLUS software. It allows distinguishing between the distributions of Classes C and D. The objective of the present study is to discriminate between the LN3 distribution and that of Class C of regularly varying distributions (heavier tail) and D of subexponential distributions (lighter tail) and then to improve the current version of the DSS. The power of several normality tests is evaluated for log-transformed variates using a Monte Carlo approach for different alternative hypothesis. The Jarque-Bera test has been found the most powerful on transformed data. Results show a strong dependence between the values of the parameters and the power of the test as well as the quantile estimation errors. Results lead to the development of a LN3 goodness-of-fit procedure, based on the coefficient of variation, the coefficient of skewness and the Jarque-Bera normality test. This procedure will be added to the Decision Support System of the HYFRAN-PLUS software.