Data analysis

This part gives an overview of the content of the statistical toolbox that may be used to build uncertainty models according to the available data.

Comparison of two samples

• Using QQ-plot to compare two samples
• Kolmogorov-Smirnov two samples test

Estimation of a parametric model

• Empirical cumulative distribution function
• Kernel smoothing
• Maximum Likelihood Principle
• Parametric Estimation

Calibration

• Bayesian calibration
• Code calibration
• Gaussian calibration
• The Metropolis-Hastings Algorithm

Analysis of the goodness of fit of a parametric model

• Graphical goodness-of-fit tests
• Chi-squared goodness of fit test
• Kolmogorov-Smirnov fitting test
• Cramer-Von Mises goodness-of-fit test
• Anderson-Darling goodness-of-fit test
• Akaike Information Criterion (AIC)
• Bayesian Information Criterion (BIC)

Detection and quantification of dependencies

• Pearson correlation coefficient
• Pearson’s correlation test
• Spearman correlation coefficient
• Spearman correlation test
• Chi-squared test for independence
• Linear regression
• Tail dependence coefficients

Estimating a quantile

• Estimation of a quantile by Wilks’ method