Discrimination between a group of three-parameter distributions for hydro-meteorological frequency modeling

Ismaila Ba,Fahim Ashkar

doi:10.1139/cjce-2017-0416

Abstract

We recommend methods of discrimination between some three-parameter distributions used in hydro-meteorological frequency modeling. Discriminations are between model pairs belonging to the group (generalized extreme value (GEV), Pearson Type III (P3), generalized logistic (GLO)). To assess the fit of these distributions to data, the Akaike information criterion, Bayesian information criterion, and (or) goodness-of-fit measures are commonly employed. However, it is difficult to estimate the discrimination power and bias of these methods when used with three-parameter distributions. Consequently, we propose two alternative tools and assess their performance. Both tools are based on a sample transformation to normality followed by applying a powerful statistic for testing normality, such as the Shapiro-Wilk or the probability plot correlation coefficient statistic. While arriving at recommendations for discriminating between the (GEV, GLO) and (P3, GLO) pairs of models, we show that the discrimination power between the P3 and GEV distributions can be rather low.

Highlights

Hydro-meteorological frequency analysis is concerned with analyzing the magnitudes of hydrometeorological events and assessing their probability of occurrence, for use in risk assessment and management
Other https://mc06.manuscriptcentral.com/cjce-pubs goodness-of-fit tests are not based on the empirical cumulative distribution function, such as the Shapiro-Wilk (SW) test for normality (Shapiro and Wilk 1965) and the probability plot correlation coefficient (PPCC) test (Filliben 1975; Vogel 1986, and others)
The focus of this study is to propose and compare practical methods of discrimination between three-parameter distributions such as generalized extreme value (GEV), P3, and generalized logistic 5 (GLO), which are important in hydrometeorological frequency modeling

Summary

Introduction

Hydro-meteorological frequency analysis is concerned with analyzing the magnitudes of hydrometeorological events and assessing their probability of occurrence, for use in risk assessment and management. These events can be floods, droughts, extreme rainfalls, or other extremes. A need exists for improved methods of selecting an appropriate statistical distribution to fit hydro-meteorological data. Such improved methods help reduce the error involved in quantile estimation. The present study focuses on a group of three-parameter distributions important in hydrometeorological frequency modeling It has the objective of recommending discrimination methods between these models. “discrimination power” and “discrimination bias”, which we will formally define

Measuring model fit

Some remarks on the discrimination between models

Discriminating between three-parameter models

Findings

Discussion and conclusion