# extreme value analysis example

So, we estimate that 99% of claims that occur result in a loss below \$13018.15, and in the cases where a claim results in a loss larger than this amount, we estimate that the expected loss will be \$21631.43. evir’s gpd method uses the max likelihood approach to estimate the parameters (shape and scale) of the GPD distribution. of this lesson that follows. Naturally Next we can try comparing the loss data to the exponential distribution using a QQplot. evir’s plot() method gives us 4 plots — excess, tail of underlying, scatter of residuals, QQplot of residuals. Finally, we'll call fmincon at each value of R10, to find the corresponding constrained maximum of the log-likelihood. Finding the lower confidence limit for R10 is an optimization problem with nonlinear inequality constraints, and so we will use the function fmincon from the Optimization Toolbox™. any sharp peaks or discontinuities to be concerned about. In this post we walked through a simple example of using EVT to model large insurance claim events in R. We used the evir package to analyse an example claims data set, and found estimates for thresholds below which a certain percentage of claims occur, and for the expected value of a loss given a claim occurs above such a threshold. Since extreme events are rare by definition, prediction of future events relies on extrapolation from a suitable model fitted to historical data. The largest function value from the previous step is the maximum value, and the smallest function value is the minimum value of the function on the given interval. This example shows how to fit the generalized extreme value distribution using maximum likelihood estimation. The Generalized Extreme Value (GEV) distribution unites the type I, type II, and type III extreme value distributions into a single family, to allow a continuous range of possible shapes. What Is Dask and How Can It Help You as a Data Scientist? is the number of widgets made and sold (in thousands) and P is the profit Now that we have fitted a GPD model to our loss data, we can use it to satisfy our objectives — an estimate for a size threshold we can set below which 99% (quantile) of claims occur, and an estimate for the expected loss above such a threshold. the graph. where x While the parameter estimates may be important by themselves, a quantile of the fitted GEV model is often the quantity of interest in analyzing block maxima data. Compare For example, the type I extreme value is the limit distribution of the maximum (or minimum) of a block of normally distributed data, as the block size becomes large. Notice that for k < 0 or k > 0, the density has zero probability above or below, respectively, the upper or lower bound -(1/k). Arce copyright 2010 (c) Sharon Walker and theDepartment of Mathematics and First, let’s load some example loss data. The shape reflects the strongly right-skewed behaviour of our data. Check Graph the function and qplot in evir creates a QQplot for threshold data against the exponential distribution. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Last Update: January 9, 2010 Leslie analysis • In addition attempted to fit a GPD to the claims severity • In our exercise, for 9 out of the 11 classes, the GPD was about as good or better than a standard loss distribution in modelling the extreme tail values of the loss severity distributions. A quick check on the graphing calculator gives a visual verification that