Extreme value analysis in engineering (largest extreme values)

Extreme value analysis deals with extreme events. In engineering, extreme value analysis is used to estimate the maximum wind speed (important for determining the maximum load on structures due to wind), the maximum river discharge or wave height (important information for the design height of dikes), maximum earthquake intensity (important input for structural mechanics), the maximum voltage level, et cetera.

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 maxima (or largest values). For mimima (or smallest values) see this R code.

The code focuses on an application of extreme value analysis in the field of engineering, namely obtaining the maximum wind speed.

The code shows how to fit a Gumbel and Weibull distribution for largest values to the wind speed data. Subsequently, the same data will be fitted with a Generalized Extreme Value (or GEV) distribution for maxima. The three extreme value distributions for largest 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 largest values fits either the Gumbel, Weibull, or Fréchet distribution for maxima.

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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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R code for fitting a multitype NHPP model to grouped temporal data

The following R code demonstrates how to fit a multitype NonHomogeneous Poisson Process (NHPP) model to grouped temporal data. Multitype Poisson processes belong to the family of marked point processes.
Note that grouped temporal data occurs when only the number of recurrences within a given time interval are known.

The R code may be used to fit 1) a multitype NHPP model with a loglinear intensity function, with the intensity at time t defined by  e^{\gamma_{0} + \gamma_{1}t}, or 2) a multitype NHPP model with a power law intensity function, with the intensity at time t defined by  \gamma_{0}*t^{\gamma_{1}}.

Furthermore, the R code also shows how to fit a multitype Homogeneous Poisson Process (HPP) model to grouped temporal data.

NHPP multitype grouped

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R code for fitting a multitype NHPP model to temporal data

The following R code demonstrates how to fit a multitype NonHomogeneous Poisson Process (NHPP) model to temporal data. Multitype Poisson processes belong to the family of marked point processes.

The R code may be used to fit 1) a multitype NHPP model with a loglinear intensity function, with the intensity at time t defined by  e^{\gamma_{0} + \gamma_{1}t}, or 2) a multitype NHPP model with a power law intensity function, with the intensity at time t defined by  \gamma_{0}*t^{\gamma_{1}}.

Furthermore, the R code also shows how to fit a multitype Homogeneous Poisson Process (HPP) model to temporal data.

NHPP multitype

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R code for fitting a nonhomogeneous temporal Poisson process model using the spatstat package

In my previous blog post I showed how to fit power and loglinear nonhomogeneous Poisson process (NHPP) models to temporal data.

The following R code fits these same two models, but this time using the spatstat package.

NHPP spatstat

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