Left-censored data with one or more detection limits (DLs) often arise in environmental contexts. The computational procedure for the calculation of maximum likelihood estimators of the parameter for Type I multiply left-censored data from underlying exponential distribution is suggested and used considering various numbers of DLs. The expected Fisher information measure (FIM) is analytically determined and its performance is compared with sample (observed) FIM using simulations. Simulations are focused primarily on the properties of estimators for small sample sizes. Moreover, the simulations follow the possible applications of the results in the statistical analysis of real chemical data.
Due to recent occurrences of extreme hydrological events in Central Europe, there is an increasing interest in more accurate prediction of return levels of such events. The precipitation records from six ombrographic stations operated by the Czech Hydrometeorological Institute were analysed in order to estimate the intensity-duration-frequency. Although the longest rainfall series consists of more than 40 years of measurements, the data set also contains records from newly established stations with only short-time series available. The impact of the series length on the estimation quality is part of this study. Parametric and nonparametric approaches to drawing samples are assumed. In the first case, we consider a threshold model and we estimate the unknown parameters using maximum likelihood and probability weighted moments methods. In the latter case, k largest order statistics are considered and the bootstrap methodology is applied as a resampling technique together with the moment estimator of extreme value index.
Precipitation records from six stations of the Czech Hydrometeorological Institute were subject to statistical analysis with the objectives of updating the intensity-duration-frequency (IDF) curves, by applying extreme value distributions, and comparing the updated curves against those produced by an empirical procedure in 1958. Another objective was to investigate differences between both sets of curves, which could be explained by such factors as different measuring instruments, measuring stations altitudes and data analysis methods. It has been shown that the differences between the two sets of IDF curves are significantly influenced by the chosen method of data analysis.
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