MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles

The choice of a probability distribution function and confidence interval estimated design values have long been interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) has developed for application hydrology, its maximum likelihood estimation (MLE)-based parameter method asymptotic variance quantiles not well documented. In this study, MLE was used to estimate parameters intervals FPEG distribution. This entails variances quantile estimators. consisted set four equations which, after algebraic simplification, were solved using three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix Fisher’s expected matrix, derivatives with respect derived. applied annual precipitation data from Weihe watershed, China determined. Results showed that good candidate model can provide guidance estimating values.