######################################################################### ### Extreme value theory - Exercise sheet 1 ### ### SS 2017 Dr. Jürgen Kampf ### ######################################################################### ### Exercise 3 ############## z=1000 # Number of repeatations of the random experiment n=1 n=2 n=10 n=1000 n=10^5 RandomNumbers=array(rnorm(n*z),dim=c(z,n)) # Generate an array of normal distributed random numbers. Maxima=apply(RandomNumbers,1,max) # Compute the row-wise maximum. plot(ecdf(Maxima)) plot(density(Maxima)) # Plot empirical cumulative distribution functionand an # density estimate of the sample # in order to get an approximation of the cumulative distribution # function and the density. # We observe that the numbers on the x-axis get larger and larger, while the shape of the # empirical cumulative distribution function hardly changes. So the Gaussian distribution # lies in the MDA of the Gumbel distributions whose shape is very similar to that of the # Gaussian distribution. # At the density plot we observe however an asymmetry -- we have outliers to the # right, but not to the left.