Abstract
Abstract. The coefficient of L-variation (L-CV) is commonly used in statistical hydrology, in particular in regional frequency analysis, as a measure of steepness for the frequency curve of the hydrological variable of interest. As opposed to the point estimation of the L-CV, in this work we are interested in the estimation of the interval of values (confidence interval) in which the L-CV is included at a given level of probability (confidence level). Several candidate distributions are compared in terms of their suitability to provide valid estimators of confidence intervals for the population L-CV. Monte-Carlo simulations of synthetic samples from distributions frequently used in hydrology are used as a basis for the comparison. The best estimator proves to be provided by the log-Student t distribution whose parameters are estimated without any assumption on the underlying parent distribution of the hydrological variable of interest. This estimator is shown to also outperform the non parametric bias-corrected and accelerated bootstrap method. An illustrative example of how this result can be used in hydrology is presented, namely in the comparison of methods for regional flood frequency analysis. In particular, it is shown that the confidence intervals for the L-CV can be used to assess the amount of spatial heterogeneity of flood data not explained by regionalization models.
Highlights
It is well known that the sample coefficient of variation (CV), i.e., the ratio of standard deviation to the mean of a series of data, exhibits substantial bias and variance when samples are small or belong to highly skewed populations (Vogel and Fennessey, 1993)
The simple examples provided here intend to illustrate the method. They show that L-CV confidence intervals allow one to analyse in a consistent way very different approaches such as those based on site grouping and those that allow for the continuous variability of L-CV, for which standard techniques as homogeneity tests would be meaningless
– the validity of the confidence intervals for the L-CV provided by these distributions is checked through uniformity plots and the Anderson-Darling test statistic;
Summary
It is well known that the sample coefficient of variation (CV), i.e., the ratio of standard deviation to the mean of a series of data, exhibits substantial bias and variance when samples are small or belong to highly skewed populations (Vogel and Fennessey, 1993). This is the problem that is normally en-. The most immediate advantage of using confidence intervals, as opposed to point estimates, is that they clearly indicate the reliability of the estimate, given by the confidence level.
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