Monte-Carlo-Simulation , Wahrscheinlichkeitsverteilung , Statistischer Test
Keywords (English):
Monte Carlo simulation , Non-normal multivariate data , Skewness and kurtosis
Abstract:
Many inferential statistical tests require that the observed variables have a normal distribution. Monte Carlo simulations are used to investigate the effect of violating this assumption and require an algorithm that generates samples from non-normal distributions, thereby controlling correlations among random variables, the marginal distributions, and the multivariate distribution. Most previously used algorithms only allow control over the correlations and the marginals, but recent results show that the robustness of certain methods depends on the multivariate distribution as well. In my thesis, I suggest a new method to generate samples from non-normal distributions that allows manipulations of all three parameters simultaneously. The algorithm jointly controls the correlation matrix, central moments of the marginals, and the multivariate distribution. Additionally, I also show that the multivariate distribution has a distinct impact on the robustness of a structural equation model, whereas extraction criteria for exploratory factor analysis are unaffected by the underlying distribution.
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