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.
Abstract. Long-lasting research infrastructures covering the research areas of atmospheric chemistry, meteorology and climatology are of highest importance. The Atmospheric Station (AS) Křešín u Pacova, central Czech Republic, is focused on monitoring of the occurence and long-range transport of greenhouse gases, atmospheric aerosols, selected gaseous atmospheric pollutants and basic meteorological characteristics. The AS and its 250 m tall tower was built according to the recommendations of the Integrated Carbon Observation System (ICOS) and cooperates with numerous national and international projects and monitoring programmes. First measurements conducted at ground started in 2012, vertical profile measurements were added in 2013. A seasonal variability with slightly higher autumn and winter concentrations of elemental and organic carbon was revealed. The suitability of the doubly left-censored Weibull distribution for modelling and interpretation of elemental carbon concentrations, which are often lower than instrumental quantification limits, was verified. Initial data analysis also suggests that in summer, the tower top at 250 m is frequently above the nocturnal surface inversions, thus being decoupled from local influences.
Type I doubly left-censored data often arise in environmental studies. In this paper, the power of the most frequently used goodness-of-fit tests (Kolmogorov-Smirnov, Cramér-von Mises, Anderson-Darling) is studied considering various sample sizes and degrees of censoring. Attention is paid to testing of the composite hypothesis that the data has a specific distribution with unknown parameters, which are estimated using the maximum likelihood method. Performance of the tests is assessed by means of Monte Carlo simulations for several distributions, specifically the Weibull, lognormal and gamma distributions, which are among the most frequently used distributions for modelling of environmental data. Finally, the tests are used for identification of the distribution of musk concentrations if fish tissue.
Left-censored data with one or more detection limits occur frequently in many application areas. In this paper, the computational procedure for calculation of maximum likelihood estimates of the parameters for type I multiply left-censored data from underlying Weibull distribution is suggested and used considering various numbers of detection limits. The expected Fisher information matrix is analytically determined and its performance is compared with sample (observed) Fisher information matrix using simulations. Simulations are focused primarily on the properties of estimators for small sample sizes. Real data illustration is included.
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