R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for a HTML browser interface to help.
Type 'q()' to quit R.

> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("fExtremes-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('fExtremes')
Loading required package: fBasics

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fBasics: Markets, Basic Statistics, Date and Time
Loading required package: fCalendar

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fCalendar: Markets, Basic Statistics, Date and Time
Loading required package: fSeries

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fSeries: The Dynamical Process Behind Financial Markets
Loading required package: fMultivar
Loading required package: mgcv
This is mgcv 1.3-1 
Loading required package: nnet

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fSeries 2: Multivariate Financial Markets Analysis

Rmetrics, (C) 1999-2004, Diethelm Wuertz, GPL
fExtremes: Beyond the Sample: Dealing with Extreme Values
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "A2-ExtremesPlots"
> 
> ### * A2-ExtremesPlots
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ExtremesPlots
> ### Title: Explorative Data Analysis
> ### Aliases: ExtremesPlots emdPlot qqPlot qqbayesPlot qPlot mePlot mrlPlot
> ###   mxfPlot msratioPlot recordsPlot ssrecordsPlot xacfPlot
> ###   interactivePlot gridVector
> ### Keywords: hplot
> 
> ### ** Examples
>  
> ## emdPlot -
>    xmpExtremes("\nStart: Empirical Distribution Function >")
>    # Danish fire insurance data show Pareto tail behaviour:
>    par(mfrow = c(2, 2))
>    data(danish)
>    emdPlot(danish, plottype = "xy", labels = FALSE)
>    title(xlab = "x", ylab = "1-F(x)", main = "Danish Fire")   
>    # BMW Stocks:
>    data(bmw)
>    emdPlot(bmw, plottype = "xy", labels = FALSE)
>    title(xlab = "x", ylab = "1-F(x)", main = "BMW Stocks")  
>    # Simulated Student-t:
>    emdPlot(rt(5000, 4), plottype = "xy") 
>  
> ## qqPlot -
>    xmpExtremes("\nNext: Quantile-Quantile Plot >")
>    # QQ-Plot of Simulated Normal rvs:
>    par(mfrow = c(2, 2))
>    set.seed(4711)
>    qqPlot(rnorm(5000))
[1] "Normal QQ-Plot"
>    text(-3.5, 3, pos = 4, "Simulated Normal rvs")
>    # QQ-Plot of simulated Student-t rvs:
>    qqPlot(rt(5000, 4))
[1] "Normal QQ-Plot"
>    text(-3.5, 11.0, pos = 4, "Simulated Student-t rvs")
>    # QQ-Plot of BMW share residuals:
>    data(bmw)
>    qqPlot(bmw)
[1] "Normal QQ-Plot"
>    text(-3.5, 0.09, pos = 4, "BMW log returns")     
>    
> ## qPlot -
>    xmpExtremes("\nNext: QQ-Plot of Heavy Tails >")
>    # QQ-Plot of heavy-tailed Danish fire insurance data:
>    data(danish)
>    qPlot(danish) 
>  
> ## mePlot -
>    xmpExtremes("\nNext: Mean Excess Plot >")
>    # Sample mean excess plot of heavy-tailed Danish fire 
>    # insurance data 
>    par(mfrow = c(3, 2))
>    data(danish)
>    mePlot(danish, labels = FALSE)
>    title(xlab = "u", ylab = "e", main = "mePlot - Danish Fire Data")
>    
> ## mrlPlot -
>    xmpExtremes("\nNext: mean Residual Live Plot >")
>    # Sample mean residual live plot of heavy-tailed Danish Fire 
>    # insurance data 
>    mrlPlot(danish, labels = FALSE)
>    title(xlab = "u", ylab = "e", main = "mrlPlot - Danish Fire Data")
>  
> ## mxfPlot -
>    xmpExtremes("\nNext: Mean Excess Function Plot >")
>    # Plot the mean excess functions for randomly distributed 
>    # residuals  
>    par(mfrow = c(2, 2))
>    n = 10000    
>    set.seed(4711)
>    xlab = "Threshold: u"; ylab = "Mean Excess: e"
>    mxfPlot(rnorm(n), tail = 0.5, labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "mxf Plot - Normal DF")
>    set.seed(7138)
>    mxfPlot(rexp(n, 2), tail = 0.5, labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "mxfPlot - Exponential DF")
>    abline(1/2, 0)
>    set.seed(6952)
>    mxfPlot(rlnorm(n, 0, 2), tail = 0.5, xlim = c(0,90), 
+      ylim = c(0, 120), labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "mxfPlot - Lognormal DF")
>    set.seed(8835)
>    mxfPlot(rgpd(n, 1/2), tail = 0.10, xlim = c(0,200), 
+      ylim=c(0,200), labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "mxfPlot - Pareto")
>    abline(0, 1)  
>  
> ## msratioPlot -
>    xmpExtremes("\nNext: Maximum/Sum Ratio Plot >")
>    # Examples for Ratio of Maximum and Sum Plots:
>    par(mfrow = c(3, 2))
>    data(bmw)
>    xlab = "n"; ylab = "R(n)"
>    msratioPlot (rnorm(8000), labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "Standard Normal")
>    msratioPlot (rexp(8000), labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "Exponential")
>    msratioPlot (rt(8000, 4), labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "Student-t")
>    msratioPlot (rcauchy(8000), labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "Cauchy")
>    msratioPlot (bmw, labels = FALSE)
>    title(xlab = xlab, ylab = ylab, main = "BMW Returns")
>   
> ## recordsPlot -
>    xmpExtremes("\nNext: Records Plot >")
>    # Record fire insurance losses in Denmark
>    par(mfrow = c(2, 2))
>    data(danish)
>    recordsPlot(danish)
>    text(1, 7.9, pos = 4, "Danish Fire")
>    # BMW Stocks
>    data(bmw)
>    recordsPlot(bmw)
>    text(1, 12.8, pos = 4, "BMW Shares")
>       
> ## ssrecordsPlot -
>    xmpExtremes("\nNext: Subsample Record Plot >")
>    # Record fire insurance losses in Denmark
>    ssrecordsPlot(danish)
>    text(1, 9.2, pos = 4, "Danish Fire")
>    # BMW Stocks
>    ssrecordsPlot(bmw)
>    text(1, 10.5, pos = 4, "BMW Shares")  
>  
> ## xacfPlot -
>    xmpExtremes("\nNext: ACF Plot of Exceedences >")
>    # Plot ACF of Heights/Distances of Eceedences over threshold:
>    par(mfrow = c(2, 2))
>    data(bmw)
>    xacfPlot(bmw)
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "A3-ExtremesPreprocessing"
> 
> ### * A3-ExtremesPreprocessing
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ExtremesPreprocessing
> ### Title: Preprocessing Extreme Value Data
> ### Aliases: ExtremesPreprocessing findThreshold blocks blockMaxima
> ###   deCluster
> ### Keywords: data
> 
> ### ** Examples
>   
> ## findThreshold -
>    xmpExtremes("\nStart: Find Thresold >")
>    # Find threshold giving (at least) fifty exceedances 
>    # for Danish Fire data
>    data(danish)
>    findThreshold(danish, n = c(10, 50, 100))    
[1] 38.15439 17.06847 10.50000
>    
> ## blockMaxima -
>    xmpExtremes("\nNext: Compute Block Maxima >")
>    # Block Maxima (Minima) for the right and left tails 
>    # of the BMW log returns:
>    data(bmw)
>    par(mfrow = c(2, 1))
>    blockMaxima( bmw, block = 100)
 [1] 0.04770410 0.05777954 0.08570879 0.05814339 0.07356377 0.06627812
 [7] 0.04774362 0.03609579 0.02224307 0.02901701 0.04006161 0.02674273
[13] 0.02967623 0.02839504 0.02837364 0.02015991 0.03086640 0.06841199
[19] 0.03807012 0.06993022 0.04052802 0.04069590 0.04524335 0.04428878
[25] 0.02813696 0.02798684 0.03842747 0.03726731 0.04031627 0.02665524
[31] 0.05408877 0.05046767 0.06634279 0.09034829 0.05577568 0.06628046
[37] 0.04317288 0.04676699 0.11719179 0.08502850 0.04099124 0.02820872
[43] 0.02972372 0.05715207 0.05717683 0.03105917 0.06767476 0.08863204
[49] 0.04470772 0.04132586 0.03595831 0.05559860 0.02910799 0.06860589
[55] 0.07947459 0.06668912 0.03500941 0.03091335 0.03136727 0.02297398
[61] 0.03309369 0.01913395
>    blockMaxima(-bmw, block = 100)     
 [1] 0.05525992 0.05084288 0.06887800 0.10617520 0.05865478 0.04466626
 [7] 0.04071008 0.01930148 0.02896766 0.04122546 0.03094040 0.03465775
[13] 0.02606819 0.02535533 0.02710781 0.02185151 0.02800261 0.06955422
[19] 0.03859640 0.06807869 0.02732490 0.04194781 0.04957226 0.01821111
[25] 0.02652559 0.04541566 0.02695412 0.03051167 0.03984488 0.02648610
[31] 0.04525858 0.03236528 0.05561317 0.04609111 0.06519183 0.04880244
[37] 0.04565154 0.04148352 0.10852160 0.04256177 0.03225168 0.02308842
[43] 0.02272718 0.14061565 0.03354484 0.06611286 0.07529138 0.04328683
[49] 0.10577463 0.02295675 0.04317727 0.05806183 0.03004121 0.03973532
[55] 0.02688352 0.04001846 0.03012671 0.03412405 0.02273563 0.03490287
[61] 0.01929721 0.02014457
>  
> ## deCluster -
>    xmpExtremes("\nNext: De-Cluster Exceedences >")
>    # Decluster the 200 exceedances of a particular  
>    # threshold in the negative BMW log-return data
>    par(mfrow = c(2, 2))
>    fit = potFit(-bmw, nextremes = 200) 
>    deCluster(fit$fit$data, 30)   
 [1] 0.05525992 0.05084288 0.06689143 0.06887800 0.04688708 0.10617520
 [7] 0.05865478 0.04071008 0.02896766 0.02913723 0.04122546 0.03094040
[13] 0.02659780 0.03465775 0.02606819 0.02710781 0.06955422 0.03859640
[19] 0.03845126 0.06807869 0.02732490 0.04194781 0.02563799 0.04957226
[25] 0.03744841 0.02652559 0.03021099 0.04541566 0.02695412 0.03051167
[31] 0.03984488 0.02648610 0.04525858 0.03938106 0.03236528 0.05561317
[37] 0.03191673 0.04609111 0.06519183 0.03668970 0.03540193 0.04491698
[43] 0.04880244 0.04565154 0.04148352 0.02619353 0.10852160 0.02954286
[49] 0.03225168 0.14061565 0.02895132 0.02834847 0.03360120 0.07529138
[55] 0.04328683 0.03405556 0.02677080 0.03221330 0.10577463 0.02764203
[61] 0.05806183 0.03004121 0.03973532 0.02892858 0.02688352 0.04001846
[67] 0.03412405 0.03232889 0.03123302 0.03490287
attr(,"times")
 [1] "1973-02-05 01:00:00 CET"  "1973-07-26 02:00:00 CEST"
 [3] "1973-11-14 01:00:00 CET"  "1973-12-31 01:00:00 CET" 
 [5] "1974-05-09 01:00:00 CET"  "1974-07-05 02:00:00 CEST"
 [7] "1974-09-30 01:00:00 CET"  "1975-05-27 01:00:00 CET" 
 [9] "1976-04-06 01:00:00 CET"  "1976-07-28 02:00:00 CEST"
[11] "1976-10-12 01:00:00 CET"  "1976-11-15 01:00:00 CET" 
[13] "1977-02-18 01:00:00 CET"  "1977-07-08 02:00:00 CEST"
[15] "1977-12-06 01:00:00 CET"  "1978-06-21 02:00:00 CEST"
[17] "1979-07-11 02:00:00 CEST" "1980-01-21 01:00:00 CET" 
[19] "1980-03-18 01:00:00 CET"  "1980-06-20 02:00:00 CEST"
[21] "1980-09-08 02:00:00 CEST" "1981-01-27 01:00:00 CET" 
[23] "1981-04-29 02:00:00 CEST" "1981-06-26 02:00:00 CEST"
[25] "1981-08-25 02:00:00 CEST" "1982-04-27 02:00:00 CEST"
[27] "1982-08-17 02:00:00 CEST" "1982-09-27 01:00:00 CET" 
[29] "1983-01-24 01:00:00 CET"  "1983-07-12 02:00:00 CEST"
[31] "1984-02-09 01:00:00 CET"  "1984-03-12 01:00:00 CET" 
[33] "1984-07-05 02:00:00 CEST" "1984-10-19 01:00:00 CET" 
[35] "1985-03-25 01:00:00 CET"  "1985-07-10 02:00:00 CEST"
[37] "1985-09-13 02:00:00 CEST" "1985-11-05 01:00:00 CET" 
[39] "1986-02-27 01:00:00 CET"  "1986-04-28 02:00:00 CEST"
[41] "1986-06-03 02:00:00 CEST" "1986-07-04 02:00:00 CEST"
[43] "1986-09-05 02:00:00 CEST" "1987-02-04 01:00:00 CET" 
[45] "1987-04-27 02:00:00 CEST" "1987-06-02 02:00:00 CEST"
[47] "1987-11-09 01:00:00 CET"  "1988-03-25 01:00:00 CET" 
[49] "1988-05-11 02:00:00 CEST" "1989-10-16 01:00:00 CET" 
[51] "1990-01-04 01:00:00 CET"  "1990-02-26 01:00:00 CET" 
[53] "1990-04-23 02:00:00 CEST" "1990-09-25 02:00:00 CEST"
[55] "1991-01-14 01:00:00 CET"  "1991-02-26 01:00:00 CET" 
[57] "1991-05-17 02:00:00 CEST" "1991-06-28 02:00:00 CEST"
[59] "1991-08-19 02:00:00 CEST" "1992-05-13 02:00:00 CEST"
[61] "1992-09-24 02:00:00 CEST" "1993-01-25 01:00:00 CET" 
[63] "1993-05-14 02:00:00 CEST" "1993-07-27 02:00:00 CEST"
[65] "1993-11-22 01:00:00 CET"  "1994-06-20 02:00:00 CEST"
[67] "1994-11-23 01:00:00 CET"  "1995-03-09 01:00:00 CET" 
[69] "1995-09-22 02:00:00 CEST" "1995-10-23 01:00:00 CET" 
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "B1-GevDistribution"
> 
> ### * B1-GevDistribution
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GevDistribution
> ### Title: GEV Distributions for Extreme Value Theory
> ### Aliases: GevDistribution dgev pgev qgev rgev devd pevd qevd revd
> ### Keywords: distribution
> 
> ### ** Examples
> 
> ## *gev  -
>    xmpExtremes("\nStart: GEV Frechet >")
>    # Create and plot 1000 GEV/Frechet distributed rdv:
>    par(mfrow = c(3, 3))
>    r = rgev(n = 1000, xi = 1)
>    plot(r, type = "l", main = "GEV/Frechet Series")
>    ## Plot empirical density and compare with true density:
>    ## Omit values greater than 500 from plot
>    hist(r[r<10], n = 25, probability = TRUE, xlab = "r", 
+      xlim = c(-5, 5), ylim = c(0, 1.1), main = "Density")
>    x = seq(-5, 5, by=0.01)
>    lines(x, dgev(x, xi = 1), col = 2)
>    ## Plot df and compare with true df:
>    plot(sort(r), (1:length(r)/length(r)), 
+      xlim = c(-3, 6), ylim = c(0, 1.1),
+      cex = 0.5, ylab = "p", xlab = "q", main = "Probability")
>    q = seq(-5,5, by=0.1)
>    lines(q, pgev(q, xi=1), col=2)
> ## Compute quantiles, a test:
>    qgev(pgev(seq(-5, 5, 0.25), xi = 1), xi = 1) 
 [1] -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00
[13] -1.00 -1.00 -1.00 -1.00 -1.00 -0.75 -0.50 -0.25  0.00  0.25  0.50  0.75
[25]  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
[37]  4.00  4.25  4.50  4.75  5.00
>    
> ## *gev -
>    xmpExtremes("\nNext: GEV Gumbel >")
>    # Create and plot 1000 Gumbel distributed rdv:
>    ##> r = rgev(n = 1000, xi = 0)
>    ##> plot(r, type = "l", main = "Gumbel Series")
>    ## Plot empirical density and compare with true density:
>    ##>hist(r[abs(r)<10], nclass = 25, freq = FALSE, xlab = "r", 
>    ##>   xlim = c(-5,5), ylim = c(0,1.1), main = "Density")
>    ##>x = seq(-5, 5, by = 0.01)
>    ##>lines(x, dgev(x, xi = 0), col=2)
>    ## Plot df and compare with true df:
>    ##>plot(sort(r), (1:length(r)/length(r)), 
>    ##>  xlim = c(-3, 6), ylim = c(0, 1.1),
>    ##>   cex=0.5, ylab = "p", xlab="q", main="Probability")
>    ##>q = seq(-5, 5, by = 0.1)
>    ##>lines(q, pgev(q, xi = 0), col = 2)
>    ## Compute quantiles, a test:
>    ##>qgev(pgev(seq(-5, 5, 0.25), xi = 0), xi = 0)   
> 
> ## *gev -
>    xmpExtremes("\nNext: GEV Weibull >")
>    # Create and plot 1000 Weibull distributed rdv:
>    r = rgev(n = 1000, xi = -1)
>    plot(r, type = "l", main = "Weibull Series")
>    ## Plot empirical density and compare with true density:
>    hist(r[abs(r)<10], nclass = 25, freq = FALSE, xlab = "r", 
+      xlim=c(-5,5), ylim=c(0,1.1), main="Density")
>    x = seq(-5, 5, by=0.01)
>    lines(x, dgev(x, xi = -1), col = 2)
>    ## Plot df and compare with true df:
>    plot(sort(r), (1:length(r)/length(r)), 
+      xlim = c(-3, 6), ylim = c(0, 1.1),
+      cex = 0.5, ylab = "p", xlab = "q", main = "Probability")
>    q=seq(-5, 5, by = 0.1)
>    lines(q, pgev(q, xi = -1), col = 2)
>    ## Compute quantiles, a test:
>    qgev(pgev(seq(-5, 5, 0.25), xi = -1), xi = -1)   
 [1] -5.00 -4.75 -4.50 -4.25 -4.00 -3.75 -3.50 -3.25 -3.00 -2.75 -2.50 -2.25
[13] -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25  0.00  0.25  0.50  0.75
[25]  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00
[37]  1.00  1.00  1.00  1.00  1.00
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "B2-GevFit"
> 
> ### * B2-GevFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GevFit
> ### Title: Modelling the GEV Distribution
> ### Aliases: GevFit gevSim gevFit print.gevFit plot.gevFit summary.gevFit
> ###   gevrlevelPlot
> ### Keywords: models
> 
> ### ** Examples
> 
> ## gevSim -
> ## gevFit -
>    # Simulate GEV Data:
>    xmpExtremes("\nStart: Simulte GEV Sample >")
>    # Use default length n=1000
>    x = gevSim(model = list(shape = 0.25, location =0 , scale = 1))
>    # Fit GEV Data by Probability Weighted Moments:
>    fit = gevFit(x, type = "pwm") 
>    print(fit)

Call:
gevFit(x = x, type = "pwm")

Estimation Type: gev pwm 

Estimated Parameters:
        xi      sigma         mu 
 0.2787613  0.9333495 -0.0624307 

>    # Summarize Results:
>    par(mfcol = c(3, 2))
>    summary(fit)

Call:
gevFit(x = x, type = "pwm")

Estimation Type: gev pwm 

Estimated Parameters:
        xi      sigma         mu 
 0.2787613  0.9333495 -0.0624307 



>    
> ## gevFit -
>    # Fit GEV Data by Max Log Likelihood Method:
>    xmpExtremes("\nNext: Estimate Parameters >")
>    fit = gevFit(x, type = "mle") 
>    print(fit)

Call:
gevFit(x = x, type = "mle")

Estimation Type: gev mle 

Estimated Parameters:
         xi       sigma          mu 
 0.26399924  0.95072588 -0.05481944 

>    # Summarize Results:
>    summary(fit) 

Call:
gevFit(x = x, type = "mle")

Estimation Type: gev mle 

Estimated Parameters:
         xi       sigma          mu 
 0.26399924  0.95072588 -0.05481944 


Standard Deviations:
        xi      sigma         mu 
0.02575889 0.02788234 0.03389952 

Log-Likelihood Value:  1679.455
Type of Convergence:   0 


>     
> ## gevSim -
> ## gevFit -
>    # Simulate Gumbel Data:
>    xmpExtremes("\nNext: Simulte Gumbel Sample >")
>    # Use default length n=1000
>    ##> x = gevSim(model = list(shape = 0, location = 0, scale = 1))
>    # Fit Gumbel Data by Probability Weighted Moments:
>    ##> fit = gevFit(x, type = "pwm", gumbel = TRUE) 
>    ##> print(fit)
>    # Summarize Results:
>    ##> par(mfcol = c(3, 2))
>    ##> summary(fit)  
>    
> ## Fit Gumbel Data by Max Log Likelihood Method:
>    xmpExtremes("\nNext: Estimate Parameters >")
>    ##> fit = gevFit(x, type = "mle", gumbel = TRUE) 
>    ##> print(fit)
>    # Summarize Results:
>    ##> summary(fit)     
>    ##> xmpExtremes("Press any key to continue >") 
>    
> ## Return levels based on GEV Fit:
>    # BMW Stock Data:
>    xmpExtremes("\nNext: Compute BMW Return Levels >")
>    par(mfrow = c(2, 1))
>    data(bmw)
>    # Fit GEV to monthly Block Maxima:
>    fit = gevFit(-bmw, block = "month") 
>    # Calculate the 40 month return level
>    gevrlevelPlot(fit, k.block = 40, main = "BMW: Return Levels")   
       min          v        max 
0.06117160 0.07056898 0.08500193 
>    
> ## Return levels based on GEV Fit:
>    xmpExtremes("\nNext: Compute SIEMENS Return Levels >")
>    # Siemens Stock Data:
>    data(siemens)
>    # Fit GEV to monthly Block Maxima:
>    fit = gevFit(-siemens, block = "month") 
>    # Calculate the 40 month return level
>    gevrlevelPlot(fit, k.block = 40, main = "SIEMENS: Return Levels")
       min          v        max 
0.04983656 0.05844122 0.07224392 
>    
> ## Interactive Plot:
>    ##> par(mfrow = c(1, 1), ask = TRUE)
>    ##> plot(fit)
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "B3-GevGlmFit"
> 
> ### * B3-GevGlmFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GevGlmFit
> ### Title: Modelling the GEV Distribution including GLM
> ### Aliases: GevGlmFit gevglmFit print.gevglmFit plot.gevglmFit
> ###   summary.gevglmFit gevglmprofPlot gevglmprofxiPlot
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Simulated GEV Data:
>    xmpExtremes("\nStart: Simulte GEV Sample >")
>    x = gevSim(model = list(shape = 0.25, location = 0, scale = 1), n = 1000)
>    par(mfrow = c(2, 2))
>    plot(x, main = "Simulated GEV Data")
>    # Fit GEV Data:
>    fit = gevglmFit(x) 
>    print(fit)

Call:
gevglmFit(x = x)

Estimation Type: gevglm mle 

Estimated Parameters:
         xi       sigma          mu 
 0.26399924  0.95072588 -0.05481944 

>    # Summarize Results:
>    summary(fit, which = c(TRUE, TRUE, TRUE, FALSE))

Call:
gevglmFit(x = x)

Estimation Type: gevglm mle 

Estimated Parameters:
         xi       sigma          mu 
 0.26399924  0.95072588 -0.05481944 


Standard Deviations:
        xi      sigma         mu 
0.02575889 0.02788234 0.03389952 

Log-Likelihood Value:  1679.455
Type of Convergence:   0 


>    
> ## Simulated GEV Data:
>    xmpExtremes("\nNext: Estimate Parameters >")
>    ##> x = gevSim(model = list(shape = 0, location = 0, scale = 1), n = 1000)
>    ##> par(mfrow = c(2, 2))
>    ##> plot(x, main = "Simulated Gumbel Data")
>    # Fit GEV Data:
>    ##> fit = gevglmFit(x, gumbel = TRUE) 
>    ##> print(fit)
>    # Summarize Results:
>    ##> summary(fit, which = c(TRUE, TRUE, TRUE, FALSE))
>    
> ## Portpirie Data:
>    xmpExtremes("\nNext: Fit Portpirie Data >")
>    par(mfrow = c(2, 1))
>    data(portpirie)
>    fit = gevglmFit(portpirie[, 2])
>    gevglmprofPlot(fit, m = 10, 4.1, 5)
If routine fails, try changing plotting interval
>    title(main = "Portpirie")
>    gevglmprofxiPlot(fit, -0.3, 0.3)
If routine fails, try changing plotting interval
>    title(main = "Portpirie")
>    
> ## Interactive Plot:
>    ##> par(mfrow = c(2, 2))
>    ##> plot(fit)
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "B4-MdaPlots"
> 
> ### * B4-MdaPlots
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: MdaPlots
> ### Title: Hill and Shape Parameter Plots
> ### Aliases: MdaPlots hillPlot shaparmPlot shaparmPickands shaparmHill
> ###   shaparmDEHaan
> ### Keywords: math
> 
> ### ** Examples
> 
> ## hillPlot -
>    xmpExtremes("\nStart: Hill Estimator >")
>    # Hill plot of heavy-tailed Danish fire insurance data 
>    # and BMW stock data for estimated 0.999 quantile
>    par(mfrow = c(2, 2))
>    data(bmw)
>    hillPlot(bmw)
>    hillPlot(bmw, option = "quantile", end = 500, p = 0.999)
>    data(danish)
>    hillPlot(danish)
>    hillPlot(danish, option = "quantile", end = 500, p = 0.999)
>    
> ## shaparmPlot -
>    xmpExtremes("\nNext: Shape Parameter Plots >")
>    par(mfcol = c(3, 2), cex = 0.6)
>    data(bmw)
>    shaparmPlot(bmw)
Taildepth:  0.01 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1]  0.5224329  0.2454821 -0.0159241
[1]  0.3691800  0.1666034 -0.1255997

Taildepth:  0.02 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.3974776 0.2689212 0.1006501
[1] -0.04261406  0.22408628 -0.13792978

Taildepth:  0.03 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.5129546 0.2747539 0.1532940
[1]  0.16927388  0.24452252 -0.05654927

Taildepth:  0.04 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.3834767 0.2839799 0.1670466
[1]  0.29451502  0.25998177 -0.01256018

Taildepth:  0.05 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2589180 0.2931234 0.1720891
[1] 0.32431490 0.27114341 0.02089733

Taildepth:  0.06 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.1742259 0.3034118 0.1712146
[1] 0.26282494 0.27982851 0.04437541

Taildepth:  0.07 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.1579362 0.3124396 0.1716353
[1] 0.23192071 0.28550397 0.06847172

Taildepth:  0.08 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.1370967 0.3193746 0.1764659
[1] 0.2427135 0.2901846 0.0875348

Taildepth:  0.09 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.1262974 0.3260446 0.1800914
[1] 0.2563105 0.2945686 0.1012523

Taildepth:  0.1 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.1457659 0.3315893 0.1842549
[1] 0.2452739 0.2999479 0.1098189

$tails
 [1] 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

$lower
$lower$pickands
 [1] 0.5224329 0.3974776 0.5129546 0.3834767 0.2589180 0.1742259 0.1579362
 [8] 0.1370967 0.1262974 0.1457659

$lower$hill
 [1] 0.2454821 0.2689212 0.2747539 0.2839799 0.2931234 0.3034118 0.3124396
 [8] 0.3193746 0.3260446 0.3315893

$lower$dehaan
 [1] -0.0159241  0.1006501  0.1532940  0.1670466  0.1720891  0.1712146
 [7]  0.1716353  0.1764659  0.1800914  0.1842549


$upper
$upper$pickands
 [1]  0.36917999 -0.04261406  0.16927388  0.29451502  0.32431490  0.26282494
 [7]  0.23192071  0.24271350  0.25631053  0.24527389

$upper$hill
 [1] 0.1666034 0.2240863 0.2445225 0.2599818 0.2711434 0.2798285 0.2855040
 [8] 0.2901846 0.2945686 0.2999479

$upper$dehaan
 [1] -0.12559970 -0.13792978 -0.05654927 -0.01256018  0.02089733  0.04437541
 [7]  0.06847172  0.08753480  0.10125232  0.10981886


> 
> ## shaparmPlot -
>    xmpExtremes("\nNext: Simulated Frechet Data >")
>    par(mfcol = c(3, 2), cex = 0.6)
>    set.seed(4711)
>    x = rgev(10000, xi = 1/4)
>    shaparmPlot(x, revert = TRUE, both.tails = FALSE)
Taildepth:  0.01 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.4795354 0.2939025 0.2034202

Taildepth:  0.02 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2352240 0.3150122 0.2258588

Taildepth:  0.03 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2802439 0.3250268 0.2425888

Taildepth:  0.04 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.3174788 0.3310540 0.2553399

Taildepth:  0.05 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.3205928 0.3349187 0.2651525

Taildepth:  0.06 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.3115011 0.3416432 0.2653683

Taildepth:  0.07 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2919714 0.3481917 0.2652338

Taildepth:  0.08 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2667770 0.3546407 0.2646682

Taildepth:  0.09 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2402061 0.3610996 0.2638406

Taildepth:  0.1 
Pickands - Hill - DeckerEinmaalDeHaan: 
[1] 0.2127520 0.3674517 0.2630136

$tails
 [1] 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

$lower
$lower$pickands
 [1] 0.4795354 0.2352240 0.2802439 0.3174788 0.3205928 0.3115011 0.2919714
 [8] 0.2667770 0.2402061 0.2127520

$lower$hill
 [1] 0.2939025 0.3150122 0.3250268 0.3310540 0.3349187 0.3416432 0.3481917
 [8] 0.3546407 0.3610996 0.3674517

$lower$dehaan
 [1] 0.2034202 0.2258588 0.2425888 0.2553399 0.2651525 0.2653683 0.2652338
 [8] 0.2646682 0.2638406 0.2630136


>    lines(c(0.01, 0.1), c(4, 4), col = "steelblue3") # True Value
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "C1-GpdDistribution"
> 
> ### * C1-GpdDistribution
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GpdDistribution
> ### Title: GPD Distributions for Extreme Value Theory
> ### Aliases: GpdDistribution dgpd pgpd qgpd rgpd
> ### Keywords: distribution
> 
> ### ** Examples
> 
> ## *gpd  -
>    xmpExtremes("\nStart: Simulate GPD Distributed sample >")
>    par(mfrow = c(2, 2))
>    r = rgpd(n = 1000, xi = 1/4)
>    plot(r, type = "l", main = "GPD Series")
>    
> ## Plot empirical density and compare with true density:
> ## Omit values greater than 500 from plot
>    xmpExtremes("\nNext: Plot Empirical and True Density >")
>    hist(r, n = 50, probability = TRUE, xlab = "r", 
+      xlim = c(-5, 5), ylim = c(0, 1.1), main = "Density")
>    x = seq(-5, 5, by = 0.01)
>    lines(x, dgpd(x, xi = 1/4), col = "steelblue3")
>    
> ## Plot df and compare with true df:
>    xmpExtremes("\nNext: Plot Empirical and True Probability >")
>    plot(sort(r), (1:length(r)/length(r)), 
+      xlim = c(-3, 6), ylim = c(0, 1.1),
+      cex = 0.5, ylab = "p", xlab = "q", main = "Probability")
>    q = seq(-5, 5, by = 0.1)
>    lines(q, pgpd(q, xi = 1/4), col = "steelblue3")
>    
> ## Compute quantiles, a test:
>    xmpExtremes("\nNext: Compute Quantiles >")
>    qgpd(pgpd(seq(-1, 5, 0.25), xi = 1/4 ), xi = 1/4) 
 [1] 0.00 0.00 0.00 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
[16] 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00
>  
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "C2-GpdFit"
> 
> ### * C2-GpdFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GpdFit
> ### Title: Modelling the Generalized Pareto Distribution
> ### Aliases: GpdFit gpdSim gpdFit print.gpdFit plot.gpdFit summary.gpdFit
> ###   gpdqPlot gpdquantPlot gpdriskmeasures gpdsfallPlot gpdshapePlot
> ###   gpdtailPlot
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Load Data:
>    data(danish)
>    
> ## gpdSim - 
>    # Simulate GPD Data:
>    xmpExtremes("\nStart: Simulate a GPD Distributed Sample > ")
>    x = gpdSim(model = list(shape = 0.25, location = 0, scale = 1), n = 1000)
>    
> ## gpdFit -   
>    xmpExtremes("\nNext: Fit Simulated Data to GPD using PWM > ")
>    fit = gpdFit(x, nextremes = length(x), type = "pwm") 
>    print(fit)

Call:
gpdFit(x = x, nextremes = length(x), type = "pwm")

Estimation Type: gpd pwm 

Estimated Parameters:
       xi      beta 
0.2916836 0.9742586 

>    par(mfcol = c(4, 2), cex = 0.7)
>    summary(fit)  

Call:
gpdFit(x = x, nextremes = length(x), type = "pwm")

Estimation Type: gpd pwm 

Estimated Parameters:
       xi      beta 
0.2916836 0.9742586 


Standard Deviations:
        xi       beta 
0.04248952 0.04987430 

Log-Likelihood Value:  NA
Type of Convergence:   NA 


>    
> ## gpdFit -
>    xmpExtremes("\nNext: Fit Simulated Data to GPD using MLE > ")
>    fit = gpdFit(x, nextremes = length(x), type = "mle") 
>    print(fit)

Call:
gpdFit(x = x, nextremes = length(x), type = "mle")

Estimation Type: gpd ml 

Estimated Parameters:
       xi      beta 
0.2862946 0.9786745 

>    summary(fit) 

Call:
gpdFit(x = x, nextremes = length(x), type = "mle")

Estimation Type: gpd ml 

Estimated Parameters:
       xi      beta 
0.2862946 0.9786745 


Standard Deviations:
        xi       beta 
0.04035302 0.04940762 

Log-Likelihood Value:  1263.129
Type of Convergence:   0 


> 
> ## gpdFit - 
>    xmpExtremes("\nNext: Fit Danish Fire Data to Excess Losses over 10 > ")
>    fit = gpdFit(danish, 10, type = "mle") 
>    print(fit)

Call:
gpdFit(x = danish, threshold = 10, type = "mle")

Estimation Type: gpd ml 

Estimated Parameters:
       xi      beta 
0.4968062 6.9745523 

>    par(mfrow = c(2, 2), cex = 0.7)
>    summary(fit)  

Call:
gpdFit(x = danish, threshold = 10, type = "mle")

Estimation Type: gpd ml 

Estimated Parameters:
       xi      beta 
0.4968062 6.9745523 


Standard Deviations:
       xi      beta 
0.1362093 1.1131016 

Log-Likelihood Value:  374.893
Type of Convergence:   0 


>      
> ## gpdqPlot - 
>    xmpExtremes("\nNext: 99.5th Percentiles for Danish Fire Data > ")
>    fit = gpdFit(danish, threshold = 10, type = "mle")
>    par(mfrow = c(1, 1))
>    tail = gpdtailPlot(fit)
>    gpdqPlot(tail, 0.995)
Lower CI Estimate Upper CI 
32.59845 40.16160 54.43935 
>    title(main = "Danish Data: 99.5th Percentile") 
>         
> ## gpdquantPlot -       
>    xmpExtremes("\nNext: 99.9th Percentiles for Danish Fire Data > ")
>    par(mfrow = c(1, 1))
>    gpdquantPlot(danish, p = 0.999)
>    title(sub = "Danish Fire: GPD High Quantile") 
> 
> ## gpdsfallPlot - 
>    xmpExtremes("\nNext: Expected Shortfall for Danish Fire Data > ")
>    fit = gpdFit(danish, nextremes = floor(length(danish)/10), type = "mle")
>    par(mfrow = c(1, 1))
>    tp = gpdtailPlot(fit)
>    gpdsfallPlot(tp, 0.999)   
Lower CI Estimate Upper CI 
119.0989 270.3280 394.8755 
>    title(main = "Danish Fire: Expected Shortfall")   
>    
> ## gpdriskmeasures -
>    xmpExtremes("\nNext: Quantiles and Expected Shortfalls > ")
>    # Give estimates of 0.999 and 0.9999 quantiles - Danish Fire Date:   
>    fit = gpdFit(danish, threshold = 10, type = "mle") 
>    par(mfrow = c(1, 1))
>    gpdriskmeasures(fit, c(0.99, 0.995, 0.999, 0.9995, 0.9999))   
       p  quantile     sfall
1 0.9900  27.28488  58.21091
2 0.9950  40.16160  83.80091
3 0.9990  94.28956 191.36972
4 0.9995 134.71099 271.69948
5 0.9999 304.62448 609.36958
>   
> ## gpdshapePlot - 
>    xmpExtremes("\nNext: Shape Plot of Heavy-Tailed Simulated Data > ")
>    set.seed(4711)
>    par(mfrow = c(1, 1))
>    gpdshapePlot(gpdSim(n = 1000))
>    title(sub = "Simulated GPD", cex.sub = 0.7)   
> 
> ## gpdshapePlot - 
>    xmpExtremes("\nNext: Shape Plot of Heavy-Tailed Danish Fire Data > ")
>    par(mfrow = c(1, 1))
>    gpdshapePlot(danish)
>    title(sub = "Danish Fire", cex.sub = 0.7)
> 
> ## gpdtailPlot - 
>    xmpExtremes("\nNext: Plot Tail Estimate of Danish Fire Data >")
>    fit = gpdFit(danish, threshold = 10, type = "mle")
>    par(mfrow = c(1, 1))
>    gpdtailPlot(fit, main = "Danish Fire: GPD Tail Estimate", col = "steelblue4")  
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "C3-GpdGlmFit"
> 
> ### * C3-GpdGlmFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GpdGlmFit
> ### Title: Modelling the GPD Distribution including GLM
> ### Aliases: GpdGlmFit gpdglmFit print.gpdglmFit plot.gpdglmFit
> ###   summary.gpdglmFit gpdglmprofPlot gpdglmprofxiPlot
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Use Rain Data:
>    data(rain)
>    
> ## Fit GPD Model:
>    xmpExtremes("Start: Parameter Estimation >")
>    fit = gpdglmFit(x = rain, threshold = 10)
>    print(fit)

Call:
gpdglmFit(x = rain, threshold = 10)

Estimation Type: gpdglm mle 

Estimated Parameters:
     sigma        mle 
7.43736339 0.05049163 

>    xmpExtremes("Next: Summary Report > ")
>    
> ## Summarize Results:
>    xmpExtremes("Next: Profile Likelihood >")
>    par(mfrow = c(2, 2), cex = 0.75)
>    summary(fit, which = "all")

Call:
gpdglmFit(x = rain, threshold = 10)

Estimation Type: gpdglm mle 

Estimated Parameters:
     sigma        mle 
7.43736339 0.05049163 


Standard Deviations:
     sigma        mle 
0.23606332 0.02256987 

Log-Likelihood Value:  6123.465
Type of Convergence:   0 


>    # Profile Lielihood:
>    par(mfrow = c(2, 1), cex = 0.75)
>    gpdglmprofPlot(fit, m = 10, xlow = 55, xup = 75)
If routine fails, try changing plotting interval
>    title(main = "Rain")
>    gpdglmprofxiPlot(fit, xlow = -0.02, 0.15)
If routine fails, try changing plotting interval
>    title(main = "Rain")
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "C4-PotFit"
> 
> ### * C4-PotFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: PotFit
> ### Title: Modelling Peaks Over a Threshold
> ### Aliases: PotFit potSim potFit print.potFit plot.potFit summary.potFit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Use Danish Fire Insurance Loss Data:
>    data(danish)
>    
> ## Fit:
>    xmpExtremes("\nStart: POT Parameter Estimate >")
>    fit = potFit(danish, threshold = 10)  
>    print(fit)

Call:
potFit(x = danish, threshold = 10)

Estimation Type: pot mle 

Estimated Parameters:
        xi      sigma         mu       beta 
 0.4971518  1.1611775 -1.6962060  6.9759676 

>    
> ## Summary with Diagnostic Plots:
>    xmpExtremes("\nNext: Diagnostic Analysis >")
>    par(mfrow = c(3, 3), cex = 0.5)
>    summary(fit)

Call:
potFit(x = danish, threshold = 10)

Estimation Type: pot mle 

Estimated Parameters:
        xi      sigma         mu       beta 
 0.4971518  1.1611775 -1.6962060  6.9759676 


Standard Deviations:
       xi     sigma        mu 
0.1358752 0.6887851 3.4377409 

Log-Likelihood Value:  876.9955
Type of Convergence:   0 


> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "C5-PPFit"
> 
> ### * C5-PPFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: PPFit
> ### Title: Modelling Point Processes
> ### Aliases: PPFit ppFit print.ppFit plot.ppFit summary.ppFit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Use Rain Data:
>    data(rain)
>    
> ## Fit Point Process Model:
>    xmpExtremes("Start: Parameter Fit for Point Process > ")
>    fit = ppFit(x = rain[1:200], threshold = 10)
>    print(fit) 

Call:
ppFit(x = rain[1:200], threshold = 10)

Parameter Estimate:
        xi      sigma         mu 
32.9371305  4.6523414 -0.1348839 
>    
> ## Summarize Results:
>    xmpExtremes("Next: Diagnostic Analysis > ")
>    par(mfrow = c(2, 2), cex = 0.75)
>    summary(fit)

Call:
ppFit(x = rain[1:200], threshold = 10)

Parameter Estimate:
        xi      sigma         mu 
32.9371305  4.6523414 -0.1348839 

Standard Deviations:
       xi     sigma        mu 
5.4561755 3.1253195 0.2403443 

Log-Likelihood Value:  3.182615
Type of Convergence:   0 


>    xmpExtremes("Next: Interactive Plot > ")
>    
> ## Interactive Plot:
>    ##> par(mfrow = c(2, 2), cex = 0.75)
>    ##> plot(fit)
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "C6-RlargFit"
> 
> ### * C6-RlargFit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: RlargFit
> ### Title: Modelling the Order Statistic Model
> ### Aliases: RlargFit rlargFit print.rlargFit plot.rlargFit
> ###   summary.rlargFit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Use Venice Data:
>    data(venice)
>    
> ## Fit for the order statistic model:
>    xmpExtremes("Start: Parameter Fit for Order Statistics Model > ")
>    fit = rlargFit(venice[, 2:4], r = 3)
>    fit

Call:
rlargFit(x = venice[, 2:4], r = 3)

Estimation Type: mle rlarg 

Estimated Parameters:
          xi        sigma           mu 
 -0.09747076  14.84784861 117.31166632 

>    
> ## Summarize Results:
>    xmpExtremes("Next: Diagnostic Analysis > ")
>    summary(fit) 

Call:
rlargFit(x = venice[, 2:4], r = 3)

Estimation Type: mle rlarg 

Estimated Parameters:
          xi        sigma           mu 
 -0.09747076  14.84784861 117.31166632 


Standard Deviations:
        xi      sigma         mu 
0.04029497 0.93869726 1.81148453 

Log-Likelihood Value:  515.3982
Type of Convergence:   0 

Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: 
Hit <Return> to see next plot: cleanEx(); ..naHit <Return> to see next plot: meEx <- "D1-ExtHit <Return> to see next plot: remeIndexPlots"
> 
> 
> ### * D1-ExtremeIndexPlots
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ExtremeIndexPlots
> ### Title: Extremal Index Estimation
> ### Aliases: ExtremeIndexPlots exindexPlot exindexesPlot
> ### Keywords: hplot
> 
> ### ** Examples
> 
> ## Extremal Index for the right and left tails 
> ## of the BMW log returns:
>    xmpExtremes("\nStart: Plot the Extremal Index >")
>    data(bmw)
>    par(mfrow = c(2, 2), cex = 0.7)
>    exindexPlot( bmw, block = "quarter")
        N  K         un    theta2     theta
 [1,]   5  5 0.08502850 1.0000000 1.0220368
 [2,]   6  6 0.07947459 1.0000000 1.0276218
 [3,]   8  7 0.07356377 0.8750000 0.9040559
 [4,]  10  8 0.06993022 0.8000000 0.8311017
 [5,]  11  9 0.06860589 0.8181818 0.8547711
 [6,]  12 10 0.06841199 0.8333333 0.8755451
 [7,]  13 11 0.06767476 0.8461538 0.8941150
 [8,]  15 12 0.06634279 0.8000000 0.8501742
 [9,]  16 13 0.06628046 0.8125000 0.8685126
[10,]  17 14 0.06627812 0.8235294 0.8855087
[11,]  20 15 0.05909805 0.7500000 0.8111325
[12,]  21 16 0.05814339 0.7619048 0.8289841
[13,]  23 17 0.05777954 0.7391304 0.8090475
[14,]  24 18 0.05717683 0.7500000 0.8260107
[15,]  26 19 0.05700682 0.7307692 0.8097854
[16,]  28 20 0.05559860 0.7142857 0.7964470
[17,]  29 21 0.05408877 0.7241379 0.8125826
[18,]  31 22 0.05166061 0.7096774 0.8014279
[19,]  32 23 0.05128512 0.7187500 0.8169703
[20,]  33 24 0.05106974 0.7272727 0.8321155
[21,]  35 25 0.05046767 0.7142857 0.8226489
[22,]  38 26 0.04774362 0.6842105 0.7932093
[23,]  39 27 0.04770410 0.6923077 0.8080891
[24,]  40 28 0.04740888 0.7000000 0.8227289
[25,]  42 29 0.04676699 0.6904762 0.8171619
[26,]  43 30 0.04619415 0.6976744 0.8315473
[27,]  44 31 0.04524335 0.7045455 0.8457803
[28,]  46 32 0.04470772 0.6956522 0.8411246
[29,]  47 33 0.04428878 0.7021277 0.8552269
[30,]  53 34 0.04331344 0.6415094 0.7869202
[31,]  62 35 0.04132586 0.5645161 0.6972745
[32,]  64 36 0.04099796 0.5625000 0.7000752
[33,]  65 37 0.04099124 0.5692308 0.7139833
[34,]  67 38 0.04069590 0.5671642 0.7169668
[35,]  68 39 0.04052802 0.5735294 0.7308400
[36,]  69 40 0.04031627 0.5797101 0.7447417
[37,]  71 41 0.04012086 0.5774648 0.7479391
[38,]  73 42 0.04006161 0.5753425 0.7513952
[39,]  79 43 0.03901445 0.5443038 0.7166364
[40,]  81 44 0.03842747 0.5432099 0.7213444
[41,]  84 45 0.03807012 0.5357143 0.7175484
[42,]  89 46 0.03727675 0.5168539 0.6982656
[43,]  90 47 0.03726731 0.5222222 0.7119538
[44,]  92 48 0.03679377 0.5217391 0.7178373
[45,]  93 49 0.03643146 0.5268817 0.7317598
[46,]  95 50 0.03609579 0.5263158 0.7379425
[47,]  97 51 0.03595831 0.5257732 0.7443409
[48,]  99 52 0.03540772 0.5252525 0.7509631
[49,] 101 53 0.03514756 0.5247525 0.7578184
[50,] 103 54 0.03500941 0.5242718 0.7649165
[51,] 104 55 0.03452181 0.5288462 0.7797583
[52,] 107 56 0.03425181 0.5233645 0.7798859
[53,] 111 57 0.03366442 0.5135135 0.7734600
[54,] 123 58 0.03309369 0.4715447 0.7176033
[55,] 142 59 0.03136727 0.4154930 0.6386410
[56,] 148 60 0.03091335 0.4054054 0.6302252
[57,] 152 61 0.03043850 0.4013158 0.6312448
[58,] 153 62 0.03040551 0.4052288 0.6452854
[59,] 159 63 0.03002665 0.3962264 0.6386869
[60,] 165 64 0.02972372 0.3878788 0.6331032
[61,] 168 65 0.02967623 0.3869048 0.6398440
[62,] 174 66 0.02939661 0.3793103 0.6356322
[63,] 181 67 0.02910799 0.3701657 0.6287536
[64,] 182 68 0.02901701 0.3736264 0.6438596
[65,] 183 69 0.02897511 0.3770492 0.6594960
[66,] 193 70 0.02839504 0.3626943 0.6437149
[67,] 194 71 0.02837364 0.3659794 0.6599239
[68,] 198 72 0.02820872 0.3636364 0.6663709
[69,] 200 73 0.02813696 0.3650000 0.6802685
[70,] 204 74 0.02792824 0.3627451 0.6879089
[71,] 208 75 0.02777174 0.3605769 0.6962559
[72,] 221 76 0.02706787 0.3438914 0.6761348
[73,] 227 77 0.02674273 0.3392070 0.6800346
[74,] 232 78 0.02665524 0.3362069 0.6879523
[75,] 233 79 0.02656937 0.3390558 0.7090750
[76,] 267 80 0.02478442 0.2996255 0.6393667
[77,] 273 81 0.02467931 0.2967033 0.6483589
[78,] 299 82 0.02359398 0.2742475 0.6135391
[79,] 312 83 0.02297398 0.2660256 0.6109630
[80,] 319 84 0.02268866 0.2633229 0.6223163
[81,] 326 85 0.02224307 0.2607362 0.6354953
[82,] 342 86 0.02173349 0.2514620 0.6332502
[83,] 344 87 0.02170679 0.2529070 0.6609209
[84,] 373 88 0.02082339 0.2359249 0.6408374
[85,] 403 89 0.02015991 0.2208437 0.6265744
[86,] 407 90 0.02004808 0.2211302 0.6611411
[87,] 412 91 0.01988137 0.2208738 0.7023112
[88,] 442 92 0.01913395 0.2081448 0.7122501
[89,] 455 93 0.01893024 0.2043956 0.7722222
[90,] 556 94 0.01714157 0.1690647 0.7388529
>    exindexPlot(-bmw, block = "quarter")   
         N  K         un     theta2     theta
 [1,]    9  5 0.06955422 0.55555556 0.5676133
 [2,]   10  6 0.06887800 0.60000000 0.6163722
 [3,]   11  7 0.06807869 0.63636364 0.6573346
 [4,]   15  8 0.06519183 0.53333333 0.5538421
 [5,]   17  9 0.05806183 0.52941176 0.5528167
 [6,]   20 10 0.05561317 0.50000000 0.5249845
 [7,]   22 11 0.05525992 0.50000000 0.5279530
 [8,]   24 12 0.05188484 0.50000000 0.5309689
 [9,]   25 13 0.05084288 0.52000000 0.5554401
[10,]   28 14 0.04957226 0.50000000 0.5371479
[11,]   31 15 0.04880244 0.48387097 0.5228416
[12,]   32 16 0.04845330 0.50000000 0.5435324
[13,]   33 17 0.04743187 0.51515152 0.5634213
[14,]   35 18 0.04688708 0.51428571 0.5658987
[15,]   38 19 0.04609111 0.50000000 0.5535207
[16,]   39 20 0.04565154 0.51282051 0.5712943
[17,]   40 21 0.04541566 0.52500000 0.5885929
[18,]   42 22 0.04525858 0.52380952 0.5909984
[19,]   45 23 0.04466626 0.51111111 0.5803393
[20,]   49 24 0.04328683 0.48979592 0.5596713
[21,]   54 25 0.04194781 0.46296296 0.5323699
[22,]   59 26 0.04148352 0.44067797 0.5100027
[23,]   60 27 0.04122546 0.45000000 0.5243553
[24,]   62 28 0.04071008 0.45161290 0.5298371
[25,]   64 29 0.04001846 0.45312500 0.5352966
[26,]   66 30 0.03984488 0.45454545 0.5407453
[27,]   67 31 0.03973532 0.46268657 0.5543916
[28,]   69 32 0.03938106 0.46376812 0.5596932
[29,]   74 33 0.03859640 0.44594595 0.5419830
[30,]   78 34 0.03744841 0.43589744 0.5336061
[31,]   83 35 0.03668970 0.42168675 0.5199577
[32,]   89 36 0.03511537 0.40449438 0.5023913
[33,]   93 37 0.03490287 0.39784946 0.4978729
[34,]   95 38 0.03474840 0.40000000 0.5044870
[35,]   97 39 0.03465775 0.40206186 0.5111205
[36,]  101 40 0.03412405 0.39603960 0.5074457
[37,]  104 41 0.03378306 0.39423077 0.5092268
[38,]  106 42 0.03360120 0.39622642 0.5160658
[39,]  109 43 0.03353101 0.39449541 0.5181146
[40,]  116 44 0.03236528 0.37931034 0.5022458
[41,]  117 45 0.03232889 0.38461538 0.5137627
[42,]  118 46 0.03225168 0.38983051 0.5253993
[43,]  119 47 0.03221330 0.39495798 0.5371654
[44,]  125 48 0.03123302 0.38400000 0.5268906
[45,]  129 49 0.03051167 0.37984496 0.5259814
[46,]  132 50 0.03012671 0.37878788 0.5294738
[47,]  135 51 0.03004121 0.37777778 0.5331455
[48,]  145 52 0.02913723 0.35862069 0.5107792
[49,]  148 53 0.02896766 0.35810811 0.5151523
[50,]  149 54 0.02895132 0.36241611 0.5267584
[51,]  150 55 0.02892858 0.36666667 0.5385777
[52,]  159 56 0.02800261 0.35220126 0.5225726
[53,]  163 57 0.02764203 0.34969325 0.5244465
[54,]  164 58 0.02732490 0.35365854 0.5363747
[55,]  165 59 0.02710781 0.35757576 0.5485690
[56,]  169 60 0.02695412 0.35502959 0.5509504
[57,]  170 61 0.02688352 0.35882353 0.5635628
[58,]  177 62 0.02659780 0.35028249 0.5566761
[59,]  178 63 0.02652559 0.35393258 0.5696107
[60,]  193 64 0.02606819 0.33160622 0.5399919
[61,]  211 65 0.02505288 0.30805687 0.5076232
[62,]  214 66 0.02485020 0.30841121 0.5150980
[63,]  215 67 0.02476860 0.31162791 0.5278203
[64,]  229 68 0.02392479 0.29694323 0.5097049
[65,]  241 69 0.02356405 0.28630705 0.4983520
[66,]  246 70 0.02337980 0.28455285 0.5027888
[67,]  255 71 0.02308842 0.27843137 0.4994964
[68,]  257 72 0.02295675 0.28015564 0.5108542
[69,]  259 73 0.02273563 0.28185328 0.5227077
[70,]  263 74 0.02272718 0.28136882 0.5309486
[71,]  282 75 0.02185151 0.26595745 0.5103622
[72,]  289 76 0.02169963 0.26297578 0.5140897
[73,]  310 77 0.02111121 0.24838710 0.4944831
[74,]  314 78 0.02092427 0.24840764 0.5047865
[75,]  323 79 0.02060147 0.24458204 0.5076223
[76,]  342 80 0.02019178 0.23391813 0.4959875
[77,]  344 81 0.02014457 0.23546512 0.5114477
[78,]  384 82 0.01930148 0.21354167 0.4742776
[79,]  385 83 0.01929721 0.21558442 0.4920408
[80,]  439 84 0.01832385 0.19134396 0.4475760
[81,]  446 85 0.01821111 0.19058296 0.4597481
[82,]  469 86 0.01775376 0.18336887 0.4567505
[83,]  472 87 0.01772653 0.18432203 0.4764060
[84,]  474 88 0.01765599 0.18565401 0.4999094
[85,]  483 89 0.01745796 0.18426501 0.5191853
[86,]  518 90 0.01687691 0.17374517 0.5144854
[87,]  589 91 0.01559548 0.15449915 0.4837260
[88,]  609 92 0.01520563 0.15106732 0.5094261
[89,]  721 93 0.01341753 0.12898752 0.4759909
[90,] 1024 94 0.01051625 0.09179688 0.3844014
>    
> ## Extremal Index for the right and left tails 
> ## of the BMW log returns:
>    xmpExtremes("\nNext: Investigate Tail Depth Dependence >")
>    data(bmw)
>    exindexesPlot( bmw, block = 65)
   thresholds    theta1    theta2    theta3
1  0.04132586 0.7153971 0.5725806 0.5000000
2  0.04296787 0.7924335 0.6363636 0.5454545
3  0.04401281 0.8577933 0.6938776 0.5714286
4  0.04619415 0.8716867 0.7209302 0.5813953
5  0.04789623 0.8576253 0.7297297 0.6216216
6  0.05166061 0.8916387 0.7741935 0.6774194
7  0.05715207 0.8723940 0.7800000 0.7200000
8  0.06158756 0.8587468 0.7894737 0.6842105
9  0.06767476 0.9425858 0.8846154 0.6923077
10 0.07732352 1.0385969 1.0000000 0.7142857
>    exindexesPlot(-bmw, block = 65)   
   thresholds    theta1    theta2    theta3
1  0.04071008 0.5681169 0.4758065 0.4677419
2  0.04190987 0.5760933 0.4909091 0.5090909
3  0.04328683 0.5496640 0.4795918 0.5714286
4  0.04491698 0.5808093 0.5116279 0.6046512
5  0.04620032 0.5383842 0.4864865 0.5945946
6  0.04880244 0.5450140 0.5000000 0.5806452
7  0.05084288 0.5817480 0.5400000 0.6800000
8  0.05587633 0.6147628 0.5789474 0.6842105
9  0.06611286 0.6845915 0.6538462 0.6923077
10 0.07801705 0.5836084 0.5714286 0.7142857
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "Z1-ExtremesTools"
> 
> ### * Z1-ExtremesTools
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ExtremesTools
> ### Title: fExtremes Tools
> ### Aliases: ExtremesTools xmpExtremes xmpfExtremes
> ### Keywords: programming
> 
> ### ** Examples
> 
> ## Not run: 
> ##D ## xmpfExtremes -
> ##D    # Popup the examples menu:
> ##D    xmpfExtremes()
> ## End(Not run)
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  17.54 2.17 20.24 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')