Application of the inverse Gaussian distribution to regional flow analysis for the island of Newfoundland

This thesis analyzes how the Inverse Gaussian distribution compares to other statistical distributions for fitting flow data from Newfoundland rivers. Although the 2-parameter Inverse Gaussian distribution is as flexible as most 3-parameter distributions, it is not currently used for statistical analysis of hydrologic data. Theories are available for regression analysis as well as hypothesis testing that is based on the Inverse Gaussian assumption. -- A hydrological study of Newfoundland rivers was performed to assess application of the Inverse Gaussian distribution to flow and regional analysis techniques. For high flows, the Inverse Gaussian distribution was compared to the Generalized Extreme Value (GEV), the 3-Parameter Lognormal (3PLN), the Extreme Value (EV) and the Lognormal (LN) distributions. For low flows, comparison was made to the 3-Parameter Weibull (W3), 2-Parameter Weibull (W2), Extreme Value (EV) and the Lognormal (LN) distributions. -- The analysis confirmed the Inverse Gaussian distribution is a suitable candidate for flood analysis of high flows. However, the distribution does not perform well for low flow analysis. Using the Akaike Information Criterion (AIC) as an indicator of suitability, the Inverse Gaussian distribution is significantly better than both the 2-parameter and 3-parameter distributions considered in this analysis for high flows. The results of the study include regional flood frequency curves based on the Inverse Gaussian distribution for two distinct regions within the island of Newfoundland. These curves are suitable for use in addition to and for comparison with other regional flood analysis techniques for Newfoundland streamflow data. -- There are two main recommendations derived from this study. The first is to apply the Inverse Gaussian distribution to streamflow data in areas other than the island of Newfoundland. Such application of the distribution to both high and low flows of other areas would determine if the suitability for high flows, or the inappropriateness for low flows, is limited to Newfoundland streamflow data. The second main recommendation is to develop an approximation for the inverse of the Inverse Gaussian distribution, similar to the approximation for the more popular Gaussian, or Normal distribution. Such an approximation would enhance the use and capabilities of the Inverse Gaussian distribution in flood frequency analysis, as well as many other statistical applications where the inverse of this robust distribution is required