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pbrod
9 years ago
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%% CHAPTER5 contains the commands used in Chapter 5 of the tutorial
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%
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% CALL: Chapter5
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%
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% Some of the commands are edited for fast computation.
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% Each set of commands is followed by a 'pause' command.
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%
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% Tested on Matlab 5.3
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% History
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% Added Return values by GL August 2008
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% Revised pab sept2005
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% Added sections -> easier to evaluate using cellmode evaluation.
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% Created by GL July 13, 2000
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% from commands used in Chapter 5
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%
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%% Chapter 5 Extreme value analysis
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%% Section 5.1 Weibull and Gumbel papers
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## CHAPTER5 contains the commands used in Chapter 5 of the tutorial
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#
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# CALL: Chapter5
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#
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# Some of the commands are edited for fast computation.
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# Each set of commands is followed by a 'pause' command.
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#
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# Tested on Matlab 5.3
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# History
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# Added Return values by GL August 2008
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# Revised pab sept2005
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# Added sections -> easier to evaluate using cellmode evaluation.
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# Created by GL July 13, 2000
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# from commands used in Chapter 5
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#
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## Chapter 5 Extreme value analysis
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## Section 5.1 Weibull and Gumbel papers
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from __future__ import division
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import numpy as np
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import scipy.interpolate as si
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from wafo.plotbackend import plotbackend as plt
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import wafo.data as wd
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import wafo.objects as wo
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import wafo.stats as ws
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import wafo.kdetools as wk
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pstate = 'off'
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% Significant wave-height data on Weibull paper,
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clf
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Hs = load('atlantic.dat');
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wei = plotweib(Hs)
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wafostamp([],'(ER)')
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disp('Block = 1'),pause(pstate)
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%%
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% Significant wave-height data on Gumbel paper,
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clf
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gum=plotgumb(Hs)
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wafostamp([],'(ER)')
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disp('Block = 2'),pause(pstate)
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%%
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% Significant wave-height data on Normal probability paper,
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plotnorm(log(Hs),1,0);
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wafostamp([],'(ER)')
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disp('Block = 3'),pause(pstate)
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%%
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% Return values in the Gumbel distribution
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clf
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T=1:100000;
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sT=gum(2) - gum(1)*log(-log(1-1./T));
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semilogx(T,sT), hold
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N=1:length(Hs); Nmax=max(N);
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plot(Nmax./N,sort(Hs,'descend'),'.')
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title('Return values in the Gumbel model')
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xlabel('Return period')
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ylabel('Return value')
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wafostamp([],'(ER)')
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disp('Block = 4'),pause(pstate)
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%% Section 5.2 Generalized Pareto and Extreme Value distributions
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%% Section 5.2.1 Generalized Extreme Value distribution
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% Empirical distribution of significant wave-height with estimated
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% Generalized Extreme Value distribution,
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gev=fitgev(Hs,'plotflag',2)
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wafostamp([],'(ER)')
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disp('Block = 5a'),pause(pstate)
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clf
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x = linspace(0,14,200);
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plotkde(Hs,[x;pdfgev(x,gev)]')
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disp('Block = 5b'),pause(pstate)
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% Analysis of yura87 wave data.
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% Wave data interpolated (spline) and organized in 5-minute intervals
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% Normalized to mean 0 and std = 1 to get stationary conditions.
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% maximum level over each 5-minute interval analysed by GEV
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xn = load('yura87.dat');
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XI = 0:0.25:length(xn);
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N = length(XI); N = N-mod(N,4*60*5);
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YI = interp1(xn(:,1),xn(:,2),XI(1:N),'spline');
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YI = reshape(YI,4*60*5,N/(4*60*5)); % Each column holds 5 minutes of
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% interpolated data.
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Y5 = (YI-ones(1200,1)*mean(YI))./(ones(1200,1)*std(YI));
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Y5M = max(Y5);
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Y5gev = fitgev(Y5M,'method','mps','plotflag',2)
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wafostamp([],'(ER)')
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disp('Block = 6'),pause(pstate)
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%% Section 5.2.2 Generalized Pareto distribution
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% Exceedances of significant wave-height data over level 3,
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gpd3 = fitgenpar(Hs(Hs>3)-3,'plotflag',1);
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wafostamp([],'(ER)')
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%%
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figure
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% Exceedances of significant wave-height data over level 7,
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gpd7 = fitgenpar(Hs(Hs>7),'fixpar',[nan,nan,7],'plotflag',1);
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wafostamp([],'(ER)')
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disp('Block = 6'),pause(pstate)
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%%
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%Simulates 100 values from the GEV distribution with parameters (0.3, 1, 2), then estimates the
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%parameters using two different methods and plots the estimated distribution functions together
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%with the empirical distribution.
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Rgev = rndgev(0.3,1,2,1,100);
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gp = fitgev(Rgev,'method','pwm');
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gm = fitgev(Rgev,'method','ml','start',gp.params,'plotflag',0);
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x=sort(Rgev);
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plotedf(Rgev,gp,{'-','r-'});
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hold on
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plot(x,cdfgev(x,gm),'--')
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hold off
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wafostamp([],'(ER)')
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disp('Block =7'),pause(pstate)
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%%
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% ;
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Rgpd = rndgenpar(0.4,1,0,1,100);
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plotedf(Rgpd);
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hold on
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gp = fitgenpar(Rgpd,'method','pkd','plotflag',0);
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x=sort(Rgpd);
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plot(x,cdfgenpar(x,gp))
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% gm = fitgenpar(Rgpd,'method','mom','plotflag',0);
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% plot(x,cdfgenpar(x,gm),'g--')
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gw = fitgenpar(Rgpd,'method','pwm','plotflag',0);
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plot(x,cdfgenpar(x,gw),'g:')
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gml = fitgenpar(Rgpd,'method','ml','plotflag',0);
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plot(x,cdfgenpar(x,gml),'--')
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gmps = fitgenpar(Rgpd,'method','mps','plotflag',0);
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plot(x,cdfgenpar(x,gmps),'r-.')
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hold off
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wafostamp([],'(ER)')
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disp('Block = 8'),pause(pstate)
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%%
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% Return values for the GEV distribution
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T = logspace(1,5,10);
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[sT, sTlo, sTup] = invgev(1./T,Y5gev,'lowertail',false,'proflog',true);
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%T = 2:100000;
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%k=Y5gev.params(1); mu=Y5gev.params(3); sigma=Y5gev.params(2);
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%sT1 = invgev(1./T,Y5gev,'lowertail',false);
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%sT=mu + sigma/k*(1-(-log(1-1./T)).^k);
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clf
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semilogx(T,sT,T,sTlo,'r',T,sTup,'r'), hold
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N=1:length(Y5M); Nmax=max(N);
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plot(Nmax./N,sort(Y5M,'descend'),'.')
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title('Return values in the GEV model')
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xlabel('Return priod')
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ylabel('Return value')
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grid on
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disp('Block = 9'),pause(pstate)
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%% Section 5.3 POT-analysis
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% Estimated expected exceedance over level u as function of u.
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clf
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plotreslife(Hs,'umin',2,'umax',10,'Nu',200);
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wafostamp([],'(ER)')
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disp('Block = 10'),pause(pstate)
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%%
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% Estimated distribution functions of monthly maxima
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%with the POT method (solid),
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% fitting a GEV (dashed) and the empirical distribution.
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% POT- method
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gpd7 = fitgenpar(Hs(Hs>7)-7,'method','pwm','plotflag',0);
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khat = gpd7.params(1);
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sigmahat = gpd7.params(2);
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muhat = length(Hs(Hs>7))/(7*3*2);
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bhat = sigmahat/muhat^khat;
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ahat = 7-(bhat-sigmahat)/khat;
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x = linspace(5,15,200);
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plot(x,cdfgev(x,khat,bhat,ahat))
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disp('Block = 11'),pause(pstate)
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%%
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% Since we have data to compute the monthly maxima mm over
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%42 months we can also try to fit a
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% GEV distribution directly:
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mm = zeros(1,41);
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for i=1:41
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mm(i)=max(Hs(((i-1)*14+1):i*14));
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end
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gev=fitgev(mm);
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hold on
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plotedf(mm)
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plot(x,cdfgev(x,gev),'--')
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hold off
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wafostamp([],'(ER)')
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disp('Block = 12, Last block'),pause(pstate)
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# Significant wave-height data on Weibull paper,
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fig = plt.figure()
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ax = fig.add_subplot(111)
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Hs = wd.atlantic()
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wei = ws.weibull_min.fit(Hs)
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tmp = ws.probplot(Hs, wei, ws.weibull_min, plot=ax)
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plt.show()
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#wafostamp([],'(ER)')
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#disp('Block = 1'),pause(pstate)
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##
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# Significant wave-height data on Gumbel paper,
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plt.clf()
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ax = fig.add_subplot(111)
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gum = ws.gumbel_r.fit(Hs)
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tmp1 = ws.probplot(Hs, gum, ws.gumbel_r, plot=ax)
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#wafostamp([],'(ER)')
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plt.show()
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#disp('Block = 2'),pause(pstate)
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##
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# Significant wave-height data on Normal probability paper,
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plt.clf()
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ax = fig.add_subplot(111)
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phat = ws.norm.fit2(np.log(Hs))
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phat.plotresq()
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#tmp2 = ws.probplot(np.log(Hs), phat, ws.norm, plot=ax)
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#wafostamp([],'(ER)')
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plt.show()
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#disp('Block = 3'),pause(pstate)
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##
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# Return values in the Gumbel distribution
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plt.clf()
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T = np.r_[1:100000]
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sT = gum[0] - gum[1] * np.log(-np.log1p(-1./T))
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plt.semilogx(T, sT)
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plt.hold(True)
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# ws.edf(Hs).plot()
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Nmax = len(Hs)
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N = np.r_[1:Nmax+1]
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plt.plot(Nmax/N, sorted(Hs, reverse=True), '.')
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plt.title('Return values in the Gumbel model')
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plt.xlabel('Return period')
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plt.ylabel('Return value')
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#wafostamp([],'(ER)')
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plt.show()
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#disp('Block = 4'),pause(pstate)
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## Section 5.2 Generalized Pareto and Extreme Value distributions
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## Section 5.2.1 Generalized Extreme Value distribution
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# Empirical distribution of significant wave-height with estimated
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# Generalized Extreme Value distribution,
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gev = ws.genextreme.fit2(Hs)
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gev.plotfitsummary()
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# wafostamp([],'(ER)')
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# disp('Block = 5a'),pause(pstate)
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plt.clf()
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x = np.linspace(0,14,200)
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kde = wk.TKDE(Hs, L2=0.5)(x, output='plot')
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kde.plot()
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plt.hold(True)
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plt.plot(x, gev.pdf(x),'--')
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# disp('Block = 5b'),pause(pstate)
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# Analysis of yura87 wave data.
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# Wave data interpolated (spline) and organized in 5-minute intervals
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# Normalized to mean 0 and std = 1 to get stationary conditions.
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# maximum level over each 5-minute interval analysed by GEV
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xn = wd.yura87()
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XI = np.r_[1:len(xn):0.25] - .99
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N = len(XI)
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N = N - np.mod(N, 4*60*5)
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YI = si.interp1d(xn[:, 0],xn[:, 1], kind='linear')(XI)
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YI = YI.reshape(4*60*5, N/(4*60*5)) # Each column holds 5 minutes of
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# interpolated data.
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Y5 = (YI - YI.mean(axis=0)) / YI.std(axis=0)
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Y5M = Y5.maximum(axis=0)
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Y5gev = ws.genextreme.fit2(Y5M,method='mps')
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Y5gev.plotfitsummary()
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#wafostamp([],'(ER)')
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#disp('Block = 6'),pause(pstate)
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## Section 5.2.2 Generalized Pareto distribution
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# Exceedances of significant wave-height data over level 3,
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gpd3 = ws.genpareto.fit2(Hs[Hs>3]-3, floc=0)
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gpd3.plotfitsummary()
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#wafostamp([],'(ER)')
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##
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plt.figure()
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# Exceedances of significant wave-height data over level 7,
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gpd7 = ws.genpareto.fit2(Hs(Hs>7), floc=7)
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gpd7.plotfitsummary()
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# wafostamp([],'(ER)')
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# disp('Block = 6'),pause(pstate)
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##
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#Simulates 100 values from the GEV distribution with parameters (0.3, 1, 2),
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# then estimates the parameters using two different methods and plots the
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# estimated distribution functions together with the empirical distribution.
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Rgev = ws.genextreme.rvs(0.3,1,2,size=100)
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gp = ws.genextreme.fit2(Rgev, method='mps');
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gm = ws.genextreme.fit2(Rgev, *gp.par.tolist(), method='ml')
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gm.plotfitsummary()
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gp.plotecdf()
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plt.hold(True)
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plt.plot(x, gm.cdf(x), '--')
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plt.hold(False)
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#wafostamp([],'(ER)')
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#disp('Block =7'),pause(pstate)
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##
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# ;
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Rgpd = ws.genpareto.rvs(0.4,0, 1,size=100)
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gp = ws.genpareto.fit2(Rgpd, method='mps')
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gml = ws.genpareto.fit2(Rgpd, method='ml')
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gp.plotecdf()
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x = sorted(Rgpd)
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plt.hold(True)
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plt.plot(x, gml.cdf(x))
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# gm = fitgenpar(Rgpd,'method','mom','plotflag',0);
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# plot(x,cdfgenpar(x,gm),'g--')
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#gw = fitgenpar(Rgpd,'method','pwm','plotflag',0);
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#plot(x,cdfgenpar(x,gw),'g:')
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#gml = fitgenpar(Rgpd,'method','ml','plotflag',0);
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#plot(x,cdfgenpar(x,gml),'--')
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#gmps = fitgenpar(Rgpd,'method','mps','plotflag',0);
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#plot(x,cdfgenpar(x,gmps),'r-.')
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plt.hold(False)
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#wafostamp([],'(ER)')
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#disp('Block = 8'),pause(pstate)
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##
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# Return values for the GEV distribution
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T = np.logspace(1, 5, 10);
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#[sT, sTlo, sTup] = invgev(1./T,Y5gev,'lowertail',false,'proflog',true);
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#T = 2:100000;
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#k=Y5gev.params(1); mu=Y5gev.params(3); sigma=Y5gev.params(2);
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#sT1 = invgev(1./T,Y5gev,'lowertail',false);
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#sT=mu + sigma/k*(1-(-log(1-1./T)).^k);
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plt.clf()
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#plt.semilogx(T,sT,T,sTlo,'r',T,sTup,'r')
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#plt.hold(True)
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#N = np.r_[1:len(Y5M)]
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#Nmax = max(N);
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#plot(Nmax./N, sorted(Y5M,reverse=True), '.')
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#plt.title('Return values in the GEV model')
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#plt.xlabel('Return priod')
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#plt.ylabel('Return value')
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#plt.grid(True)
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#disp('Block = 9'),pause(pstate)
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## Section 5.3 POT-analysis
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# Estimated expected exceedance over level u as function of u.
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plt.clf()
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mrl = ws.reslife(Hs,'umin',2,'umax',10,'Nu',200);
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mrl.plot()
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#wafostamp([],'(ER)')
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#disp('Block = 10'),pause(pstate)
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##
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# Estimated distribution functions of monthly maxima
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#with the POT method (solid),
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# fitting a GEV (dashed) and the empirical distribution.
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# POT- method
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gpd7 = ws.genpareto.fit2(Hs(Hs>7)-7, method='mps', floc=0)
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khat, loc, sigmahat = gpd7.par
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muhat = len(Hs[Hs>7])/(7*3*2)
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bhat = sigmahat/muhat**khat
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ahat = 7-(bhat-sigmahat)/khat
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x = np.linspace(5,15,200);
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plt.plot(x,ws.genextreme.cdf(x, khat,bhat,ahat))
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# disp('Block = 11'),pause(pstate)
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##
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# Since we have data to compute the monthly maxima mm over
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#42 months we can also try to fit a
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# GEV distribution directly:
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mm = np.zeros((1,41))
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for i in range(41):
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mm[i] = max(Hs[((i-1)*14+1):i*14])
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gev = ws.genextreme.fit2(mm)
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plt.hold(True)
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gev.plotecdf()
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plt.hold(False)
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#wafostamp([],'(ER)')
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#disp('Block = 12, Last block'),pause(pstate)
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