Extreme value analysis in engineering (smallest extreme values)

Extreme value analysis deals with extreme events. In engineering, extreme value analysis is used to estimate the minimum strength of materials, the minimum life time of a component, the minimum surrounding/outside temperature, or the minimum load at which a crack will develop, just to name a few.

The following code may be used for fitting extreme value models in R. Note, however, that the R code is restricted to the analysis of minima (or smallest values). For maxima (or largest values) see this R code.

The code focuses on an application of extreme value analysis in the field of engineering, namely obtaining the minimum breaking strength of a chain.

The code shows how to fit a Gumbel and Weibull distribution for smallest values to the breaking strength data. Subsequently, the same data will be fitted with a Generalized Extreme Value (or GEV) distribution for minima. The three extreme value distributions for smallest values (i.e., Gumbel, Weibull, and Fréchet distribution) are all family members of the GEV distribution. The code will demonstrate that a GEV model for smallest values fits either the Gumbel, Weibull, or Fréchet distribution for minima.

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