Abstract
The principle of maximum entropy (POME) has been used for a variety of applications in hydrology, however it has not been used in confidence interval estimation. Therefore, the POME was employed for confidence interval estimation for precipitation quantiles in this study. The gamma, Pearson type 3 (P3), and extreme value type 1 (EV1) distributions were used to fit the observation series. The asymptotic variances and confidence intervals of gamma, P3, and EV1 quantiles were then calculated based on POME. Monte Carlo simulation experiments were performed to evaluate the performance of the POME method and to compare with widely used methods of moments (MOM) and the maximum likelihood (ML) method. Finally, the confidence intervals T-year design precipitations were calculated using the POME for the three distributions and compared with those of MOM and ML. Results show that the POME is superior to MOM and ML in reducing the uncertainty of quantile estimators.
Highlights
One of the objectives of hydrological frequency analysis is to estimate the magnitude of a hydrologic event with a given return period [1]
The results show that the standard errors and confidence interval widths of quantile estimators obtained by principle of maximum entropy (POME) were smaller than those obtained by the MOM and the maximum likelihood (ML) methods with the exception of the results of
The POME method was applied for the estimation of the asymptotic variances and confidence intervals of quantiles, and the corresponding calculation formulas for gamma, Pearson type 3 (P3), and extreme value type 1 (EV1) distributions based on the POME method were deduced
Summary
One of the objectives of hydrological frequency analysis is to estimate the magnitude of a hydrologic event with a given return period [1]. Due to limited data records, inappropriate assumption regarding the parent distribution, and errors associated with parameters estimation, there are inevitably uncertainties in this estimation [2,3]. A point estimate of quantile corresponding to a desired return period is usually not enough because it cannot adequately describe the reliability of the estimation. Confidence interval is a convenient approach to quantifying the uncertainty of the estimates and provides more information than just a point estimate or its standard error [4]. The calculation of confidence interval requires a standard error of quantile estimator, and several methods have been proposed for determining such standard error. Hoshi and Barges derived the expressions for calculating the sampling variances and covariances of log-Pearson type 3 (P3)
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