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Archimedean copulas are one of the most known classes of copulas. They allow modeling the dependencies between variables with small number of parameters. This paper presents a method designated to generate multivariate samples of the same distribution like primary sample with Archimedean copulas. Such generator may be used in Monte Carlo investigations to create multivariate samples. Apart from theoretical considerations there are presented the examples of application of the method. All the calculations were carried out with R 2.15.0 packages.

One of the crucial problems in multiple-model approach of the regression is estimation of optimal number of base models. If the quantity is too low – it increases the prediction error whereas too high number of models increases time and complication of calculations. Unfortunately, the estimation of the quantity of base models based on the analysis of prediction error can lead to its overestimation. This paper proposes a formal approach where the predictions obtained with the models aggregated from different number of base models are compared. In this approach both: parametric and permutation tests were applied with the empirical data from petroleum industry. Jednym z kluczowych problemów w wielomodelowym podejściu do zagadnienia regresji jest estymacja optymalnej ilości modeli bazowych. Jeśli ich ilość jest zbyt mała – rośnie błąd predykcji, zbyt duża ilość powiększa czas i komplikację obliczeń. Niestety estymacja tej ilości na podstawie analizy błędu predykcji może prowadzić do jej przeszacowania. W artykule proponuje się formalne podejście, w którym porównywane są wyniki prognoz otrzymanych z modeli zagregowanych z różnej liczby modeli bazowych. W tym przypadku wykorzystane zostały zarówno testy parametryczne jak i testy permutacyjne, a jako dane testowe: dane empiryczne wykorzystywane w przemyśle rafineryjnym.

An indication of correlation between dependent variable and predictors is a crucial point in building statistical regression model. The test of Pearson correlation coefficient – with relatively good power – needs to fulfill the assumption about normal distribution. In other cases only non-parametric tests can be used. This article presents a possibility and advantages of permutation tests with the discussion about proposed test statistics. The power of proposed tests was estimated on the basis of Monte Carlo experiments. The investigations were carried out for real data – a sample of refinery process parameters, where the indication of changes in correlation, even for sample with small size is very important. It creates an opportunity to react to changes and update statistical models quickly and keep acceptable quality of prediction