[Robast-commits] r549 - in branches/robast-0.9/pkg: . ROptEst/R ROptEstOld ROptRegTS/R RobExtremes/R RobExtremes/inst RobExtremes/inst/AddMaterial
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Wed Jan 23 16:17:13 CET 2013
Author: ruckdeschel
Date: 2013-01-23 16:17:13 +0100 (Wed, 23 Jan 2013)
New Revision: 549
Added:
branches/robast-0.9/pkg/RobExtremes/inst/AddMaterial/
branches/robast-0.9/pkg/RobExtremes/inst/AddMaterial/comment.txt
Removed:
branches/robast-0.9/pkg/RandVar-check-output.txt
branches/robast-0.9/pkg/RobExtremes/R/comment.txt
Modified:
branches/robast-0.9/pkg/ROptEst/R/leastFavorableRadius.R
branches/robast-0.9/pkg/ROptEst/R/radiusMinimaxIC.R
branches/robast-0.9/pkg/ROptEstOld/NAMESPACE
branches/robast-0.9/pkg/ROptRegTS/R/AllClass.R
branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R
branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R
branches/robast-0.9/pkg/RobExtremes/R/WeibullFamily.R
Log:
RobExtremes: fixed bugs in GEV-, GPareto-, and WeibullFamily
ROptEst: fixed bugs in radiusMinimaxIC and in leastFavorableRadius
RobExtremes: shifted comments with auxiliary calculations to inst folder
Modified: branches/robast-0.9/pkg/ROptEst/R/leastFavorableRadius.R
===================================================================
--- branches/robast-0.9/pkg/ROptEst/R/leastFavorableRadius.R 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/ROptEst/R/leastFavorableRadius.R 2013-01-23 15:17:13 UTC (rev 549)
@@ -125,10 +125,10 @@
return(res)
}else{
if(is(L2Fam at distribution, "UnivariateDistribution")){
+ L2derivSymm <- L2Fam at L2derivSymm
+ L2derivDistrSymm <- L2Fam at L2derivDistrSymm
if((length(L2Fam at L2deriv) == 1) & is(L2Fam at L2deriv[[1]], "RealRandVariable")){
L2deriv <- L2Fam at L2deriv[[1]]
- L2derivSymm <- L2Fam at L2derivSymm
- L2derivDistrSymm <- L2Fam at L2derivDistrSymm
}else{
L2deriv <- diag(dimension(L2Fam at L2deriv)) %*% L2Fam at L2deriv
L2deriv <- RealRandVariable(Map = L2deriv at Map, Domain = L2deriv at Domain)
Modified: branches/robast-0.9/pkg/ROptEst/R/radiusMinimaxIC.R
===================================================================
--- branches/robast-0.9/pkg/ROptEst/R/radiusMinimaxIC.R 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/ROptEst/R/radiusMinimaxIC.R 2013-01-23 15:17:13 UTC (rev 549)
@@ -85,11 +85,11 @@
# print(c(rlo=loRad, Rlo=args.Ie$loRisk, rup=upRad,Rup=args.Ie$upRisk))
}else{
if(is(L2Fam at distribution, "UnivariateDistribution")){
+ L2derivSymm <- L2Fam at L2derivSymm
+ L2derivDistrSymm <- L2Fam at L2derivDistrSymm
if((length(L2Fam at L2deriv) == 1) &
is(L2Fam at L2deriv[[1]], "RealRandVariable")){
L2deriv <- L2Fam at L2deriv[[1]]
- L2derivSymm <- L2Fam at L2derivSymm
- L2derivDistrSymm <- L2Fam at L2derivDistrSymm
}else{
L2deriv <- diag(dimension(L2Fam at L2deriv)) %*% L2Fam at L2deriv
L2deriv <- RealRandVariable(Map = L2deriv at Map, Domain = L2deriv at Domain)
Modified: branches/robast-0.9/pkg/ROptEstOld/NAMESPACE
===================================================================
--- branches/robast-0.9/pkg/ROptEstOld/NAMESPACE 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/ROptEstOld/NAMESPACE 2013-01-23 15:17:13 UTC (rev 549)
@@ -1,3 +1,4 @@
+import("methods")
import("distr")
import("distrEx")
import("RandVar")
Modified: branches/robast-0.9/pkg/ROptRegTS/R/AllClass.R
===================================================================
--- branches/robast-0.9/pkg/ROptRegTS/R/AllClass.R 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/ROptRegTS/R/AllClass.R 2013-01-23 15:17:13 UTC (rev 549)
@@ -1,9 +1,4 @@
.onLoad <- function(lib, pkg){
- require("methods", character = TRUE, quietly = TRUE)
- require("distr", character = TRUE, quietly = TRUE)
- require("distrEx", character = TRUE, quietly = TRUE)
- require("RandVar", character = TRUE, quietly = TRUE)
- require("ROptEstOld", character = TRUE, quietly = TRUE)
}
# Regression type families
Deleted: branches/robast-0.9/pkg/RandVar-check-output.txt
===================================================================
--- branches/robast-0.9/pkg/RandVar-check-output.txt 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/RandVar-check-output.txt 2013-01-23 15:17:13 UTC (rev 549)
@@ -1,76 +0,0 @@
-C:\rtest\RobASt\branches\robast-0.7\pkg>R CMD check RandVar
-* checking for working pdflatex ... OK
-* using log directory 'C:/rtest/RobASt/branches/robast-0.7/pkg/RandVar.Rc
-* using R version 2.10.0 Under development (unstable) (2009-08-12 r49170)
-* using session charset: ISO8859-1
-* checking for file 'RandVar/DESCRIPTION' ... OK
-* this is package 'RandVar' version '0.7'
-* package encoding: latin1
-* checking package name space information ... OK
-* checking package dependencies ... OK
-* checking if this is a source package ... OK
-* checking for .dll and .exe files ... OK
-* checking whether package 'RandVar' can be installed ... OK
-* checking package directory ... OK
-* checking for portable file names ... OK
-* checking DESCRIPTION meta-information ... OK
-* checking top-level files ... OK
-* checking index information ... OK
-* checking package subdirectories ... OK
-* checking R files for non-ASCII characters ... OK
-* checking R files for syntax errors ... OK
-* checking whether the package can be loaded ... OK
-* checking whether the package can be loaded with stated dependencies ...
-* checking whether the name space can be loaded with stated dependencies
-* checking for unstated dependencies in R code ... OK
-* checking S3 generic/method consistency ... OK
-* checking replacement functions ... OK
-* checking foreign function calls ... OK
-* checking R code for possible problems ... OK
-* checking Rd files ... OK
-* checking Rd files against version 2 parser ... OK
-* checking Rd cross-references ... OK
-* checking for missing documentation entries ... OK
-* checking for code/documentation mismatches ... OK
-* checking Rd \usage sections ... OK
-* checking examples ... OK
-* checking differences from 'RandVar-Ex.Rout' to 'RandVar-Ex.Rout.save' .
-* checking tests ...
- Ausf³hren 'tests.R'
- Comparing 'tests.Rout' to 'tests.Rout.save' ...482c482
-< 0 0 0
----
-> 0.004 0.000 0.002
-485c485
-< 0 0 0
----
-> 0.000 0.000 0.003
-488c488
-< 0.02 0.00 0.02
----
-> 0.004 0.000 0.004
-494c494
-< 0 0 0
----
-> 0.004 0.000 0.001
-1025c1025
-< 0.02 0.00 0.01
----
-> 0.012 0.000 0.009
-1675c1675
-< 0 0 0
----
-> 0.008 0.000 0.007
-1686c1686
-< 0.08 0.00 0.07
----
-> 0.044 0.000 0.042
- OK
-* checking package vignettes in 'inst/doc' ... WARNING
-Package vignettes without corresponding PDF:
- C:/rtest/RobASt/branches/robast-0.7/pkg/RandVar/inst/doc/RandVar.Rnw
-* checking PDF version of manual ... OK
-
-WARNING: There was 1 warning, see
- C:/rtest/RobASt/branches/robast-0.7/pkg/RandVar.Rcheck/00check.log
-for details
Modified: branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R 2013-01-23 15:17:13 UTC (rev 549)
@@ -40,9 +40,8 @@
return(of.interest)
}
-.define.tau.Dtau <- function( trafo, of.interest, btq, bDq, btes,
+.define.tau.Dtau <- function(of.interest, btq, bDq, btes,
bDes, btel, bDel, p, N){
- if(is.null(trafo)){
tau <- NULL
if("scale" %in% of.interest){
tau <- function(theta){ th <- theta[1]; names(th) <- "scale"; th}
@@ -108,10 +107,7 @@
}
}
trafo <- function(x){ list(fval = tau(x), mat = Dtau(x)) }
- }else{
- if(is.matrix(trafo) & nrow(trafo) > 2) stop("number of rows of 'trafo' > 2")
- }
- return(list(trafo = trafo, tau = tau, Dtau = Dtau))
+ return(trafo)
}
## methods
@@ -200,10 +196,11 @@
D }, list(loc0 = loc, N0 = N))
}
- def <- .define.tau.Dtau( trafo, of.interest, btq, bDq, btes,
- bDes, btel, bDel, p, N)
- trafo <- def$trafo; tau <- def$tau; Dtau <- def$Dtau
-
+ if(is.null(trafo))
+ trafo <- .define.tau.Dtau(of.interest, btq, bDq, btes, bDes,
+ btel, bDel, p, N)
+ else if(is.matrix(trafo) & nrow(trafo) > 2)
+ stop("number of rows of 'trafo' > 2")
####
param <- ParamFamParameter(name = "theta", main = c(theta[2],theta[3]),
fixed = theta[1],
Modified: branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R 2013-01-23 15:17:13 UTC (rev 549)
@@ -95,10 +95,12 @@
D }, list(loc0 = loc, N0 = N))
}
- def <- .define.tau.Dtau( trafo, of.interest, btq, bDq, btes,
- bDes, btel, bDel, p, N)
+ if(is.null(trafo))
+ trafo <- .define.tau.Dtau(of.interest, btq, bDq, btes, bDes,
+ btel, bDel, p, N)
+ else if(is.matrix(trafo) & nrow(trafo) > 2)
+ stop("number of rows of 'trafo' > 2")
# code .define.tau.Dtau is in file GEVFamily.R
- trafo <- def$trafo; tau <- def$tau; Dtau <- def$Dtau
param <- ParamFamParameter(name = "theta", main = c(theta[2],theta[3]),
fixed = theta[1],
Modified: branches/robast-0.9/pkg/RobExtremes/R/WeibullFamily.R
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/R/WeibullFamily.R 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/RobExtremes/R/WeibullFamily.R 2013-01-23 15:17:13 UTC (rev 549)
@@ -95,8 +95,11 @@
D }, list(loc0 = loc, N0 = N))
}
- def <- .define.tau.Dtau( trafo, of.interest, btq, bDq, btes,
- bDes, btel, bDel, p, N)
+ if(is.null(trafo))
+ trafo <- .define.tau.Dtau(of.interest, btq, bDq, btes, bDes,
+ btel, bDel, p, N)
+ else if(is.matrix(trafo) & nrow(trafo) > 2)
+ stop("number of rows of 'trafo' > 2")
# code .define.tau.Dtau is in file GEVFamily.R
trafo <- def$trafo; tau <- def$tau; Dtau <- def$Dtau
Deleted: branches/robast-0.9/pkg/RobExtremes/R/comment.txt
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/R/comment.txt 2013-01-23 01:46:37 UTC (rev 548)
+++ branches/robast-0.9/pkg/RobExtremes/R/comment.txt 2013-01-23 15:17:13 UTC (rev 549)
@@ -1,303 +0,0 @@
-#
-# Herleitung Expected Shortfall GPD
-# a= 1-p, s=shape; scale= 1
-#q=(a^-s-1)/s
-#VaR + E(X-V|X>V)
-#q + int (X-V)_+ dP/P(X>V) = q + int (V<t) 1-P(t) dt /a=
-# [t=((-loq u)^(-s)-1)/s=(-loq u)^(-s-1)/u]
-#q+ int (V<t) 1-exp(-(1+st)^(-1/s)) dt/a =
-#q+ int_a^1 (-loq (1-u))^(-s) du/a/s = [u=e^-v]
-#q+ int_(1-a) (-loq u)^(-s-1) du/a =
-#q+ int_-log(1-a) v^(-s-1) e^-v du/a = [-logu =v]
-#(a^-s-1)/s+ (1+s(a^-s-1)/s)^(-1/s+1)/(1-s)/a=
-#(a^(-s)-1)/s+ a^(1-s)/(1-s)/a=
-#= q + s (a^(-s)-1)/s/(1-s) + 1/(1-s)=
-#= q + s q/(1-s) + 1/(1-s)=
-#= q/(1-s) + 1/(1-s)
-#
-#=gamma(1-s)/(a*s)*pgamma(-log(a),1-s,lower=F)
-#
-#mit m=loc, b=scale: ES=gamma(1-s)/(a*s)*pgamma(-log(a),1-s,lower=F)*b+m
-#
-# Herleitung L2 Abl GEVD
-## scale component
-## von Nataliya: (kontrolliert: PR)
-## -1/beta-xi*(-1/xi-1)*(x[ind]-mu)/beta^2/(1+xi*(x[ind]-mu)/beta) -
-## (x[ind]-mu)*(1+xi*(x[ind]-mu)/beta)^(-1/xi-1)/beta^2
-# [z=(x[ind]-mu)/beta]
-# = -1/beta-xi*(-1/xi-1)*z/beta/(1+xi*z) - z*(1+xi*z)^(-1/xi-1)/beta
-# = -1/beta+ (xi+1)*z/beta/(1+xi*z) - z*(1+xi*z)^(-1/xi-1)/beta
-# = (-1+ (xi+1)*z/(1+xi*z) - z*(1+xi*z)^(-1/xi-1))/beta
-# = (-(1+xi*z)+ (xi+1)*z - z*(1+xi*z)^(-1/xi))/beta/(1+xi*z)
-# = (-1-xi*z+ xi*z+z - z*(1+xi*z)^(-1/xi))/beta/(1+xi*z)
-# = (-1+z - z*(1+xi*z)^(-1/xi))/beta/(1+xi*z)
-# = (-1+z*(1-(1+xi*z)^(-1/xi)))/beta/(1+xi*z)
-# [zxi = (1+xi*z) ]
-# = (z*(1-zxi^(-1/xi))-1)/beta/zxi
-#
-#
-## shape component
-## von Nataliya: (kontrolliert: PR)
-# log(1+xi*(x[ind]-mu)/beta)/xi^2+(-1/xi-1)*(x[ind]-mu)/beta/
-# (1+xi*(x[ind]-mu)/beta) - (1+xi*(x[ind]-mu)/beta)^(-1/xi)*
-# log(1+xi*(x[ind]-mu)/beta)/xi^2 + (1+xi*(x[ind]-mu)/
-# beta)^(-1/xi-1)*(x[ind]-mu)/beta/xi
-# [z=(x[ind]-mu)/beta]
-# log(1+xi*z)/xi^2+(-1/xi-1)*z/(1+xi*z) - (1+xi*z)^(-1/xi)*
-# log(1+xi*z)/xi^2 + (1+xi*z)^(-1/xi-1)*z/xi
-# [zxi = (1+xi*z) ]
-# log(zxi)/xi^2+(-1/xi-1)*z/(zxi) - (zxi)^(-1/xi)*log(zxi)/xi^2 +
-# (zxi)^(-1/xi-1)*z/xi
-# log(zxi)/xi^2-(1+xi)*z/(zxi)/xi - (zxi)^(-1/xi)*log(zxi)/xi^2 +
-# zxi^(-1/xi-1)*z/xi
-# log(zxi)/xi^2 - (zxi)^(-1/xi)*log(zxi)/xi^2 -(1+xi)*z/(zxi)/xi +
-# zxi^(-1/xi-1)*z/xi
-# log(zxi)/xi^2 * ( 1 - (zxi)^(-1/xi)) +
-# ((zxi)^(-1/xi)-(1+xi))*z/zxi/xi
-# ( 1 - (zxi)^(-1/xi)) * ( log(zxi)/xi^2 - z/zxi/xi) - z/zxi
-# [z/zxi=zu]
-# ( 1 - (zxi)^(-1/xi)) * (log(zxi)/xi - zu)/xi - zu
-
-## umtransformation auf Quantilsskala
-# y = exp(-(1+xi z)^(-1/xi)) <=> -log y = zxi^(-1/xi)
-# <=> (-log y)^(-xi) = zxi <=> z = ((-log y)^(-xi)-1)/xi
-# => zu= z/zxi=((-log y)^(-xi)-1)/xi (-log y)^(xi)
-# =(1-(-log y)^(xi))/xi
-# 1+xi z = zxi = (1-p)^(-xi), z = [(1-p)^(-xi)-1]/xi
-## scale component
-# (z*(1-zxi^(-1/xi))-1)/beta/zxi
-# = (((-log y)^(-xi)-1)/xi*(1-((-log y)^(-xi))^(-1/xi))-1)/beta/
-# ((-log y)^(-xi))
-# = (((-log y)^(-xi)-1)/xi*(1+log y)-1)/beta ((-log y)^(xi))
-# = ((((-log y)^(xi))(-log y)^(-xi)-((-log y)^(xi)))/xi*(1+log y)
-# -((-log y)^(xi)))/beta
-# = ((1-(-log y)^(xi))/xi*(1+log y)-(-log y)^(xi))/beta
-#
-## shape component
-# ( 1 - (zxi)^(-1/xi)) * (log(zxi)/xi - zu)/xi - zu
-# = ( 1 - ((-log y)^(-xi))^(-1/xi)) * (log((-log y)^(-xi))/xi -
-# (1-(-log y)^(xi))/xi)/xi - (1-(-log y)^(xi))/xi
-# = ( 1 + log y) * (-(log(-log y)) - (1-(-log y)^(xi))/xi)/xi -
-# (1-(-log y)^(xi))/xi
-## umtransformation auf Expskala y=exp(-t), t=-log y
-## scale component
-# ((1-(-log y)^(xi))/xi*(1+log y)-(-log y)^(xi))/beta
-# = ((1-t^xi)/xi*(1-t)-t^(xi))/beta
-# = (1-t^xi-t+t^(xi+1)- xi t^xi)/beta/xi
-# = (1-(xi+1) t^xi-t+t^(xi+1))/beta/xi
-#
-## shape component
-# ( 1 + log y) * (-(log(-log y)) - (1-(-log y)^(xi))/xi)/xi -
-# (1-(-log y)^(xi))/xi
-# = ( 1 -t) * (-log(t) - (1-t^xi)/xi)/xi - (1-t^xi)/xi
-# = ( 1 -t) * (- xi log(t) - (1-t^xi))/xi^2 - xi(1-t^xi)/xi^2
-# = [xi(t-1) log(t) + (t-1)(1-t^xi) - xi(1-t^xi)]/xi^2
-# = [xi(t-1) log(t) + t-1-t^(xi+1)+t^xi - xi + xi t^xi)]/xi^2
-# = [xi(t-1) log(t) + t-t^(xi+1)+(1+xi) t^xi - (1+xi))]/xi^2
-
-
-### Integrale bei GEV - FI
-## nach exp(-t) auf 0 .. Inf zu integrieren
-## Lambda = [1-(xi+1)t^xi-t+t^(xi+1)]/(beta xi),
-## [(1+xi) (t^xi-1) +t -t^(xi+1) + xi (t-1) log(t)]/xi^2
-## Lambda Lambda' zu integrieren;
-## dazu int t^a exp(-t) = gamma(a+1),
-## int t^a log(t) exp(-t) = digamma(a+1)
-## int t^a log(t)^2 exp(-t) = trigamma(a+1)
-
-#################
-#I11 * beta^2 xi^2
-#################
-# [1-(xi+1)t^xi-t+t^(xi+1)]^2
-#= [1 + (xi+1)^2 t^(2xi) + t^2 + t^(2xi+2) -
-# -2 (xi+1)t^xi - 2t + 2t^(xi+1)
-# + 2(xi+1)t^(xi+1)-2(xi+1)t^(2xi+1)-2t^(xi+2)]
-#
-### nach Integration mit Dichte exp(-t) (Gamma!)
-#
-#= [1+(xi+1)^2 Gam(2xi+1)+Gam(3)+Gam(2xi+3)-
-# -2(xi+1)Gam(xi+1)-2Gam(2)+2Gam(xi+2)
-# +2(xi+1)Gam(xi+2)-2(xi+1)Gam(2xi+2)-2Gam(xi+3)]
-#
-#### ausnutzen Gam(a+1)= a Gam(a)
-#
-#= 1+2xi(xi+1)^2 Gam(2xi)+2+(2xi+2)(2xi+1)2xi Gam(2xi)-
-# -2(xi+1)xi Gam(xi)-2+ 2(xi+1)xi Gam(xi)
-# +2(xi+1)^2 xi Gam(xi)-2(xi+1)(1+2xi)2xi Gam(2xi)- 2*(xi+2)(xi+1)xi Gam(xi)
-#
-#### Terme sortieren
-#
-#= 1+[2xi(xi+1)^2] Gam(2xi)
-# +[-2(xi+1)xi +2(xi+1)xi +2(xi+1)^2 xi - 2 (xi+2)(xi+1)xi]Gam(xi)
-#
-#### Terme zusammenfassen
-#
-#= 1+[2xi^3-4xi^2-2xi] Gam(2xi)- [2xi^2+2xi]Gam(xi)
-#
-#################
-#I12 * beta xi^3
-#################
-#
-#[1-(xi+1)t^xi-t+t^(xi+1)] [(1+xi) (t^xi-1) +t -t^(xi+1) + xi (t-1) log(t)]
-# = 1 * [...] (=0 weil E Lambda = 0]
-# -(xi+1)^2 (t^(2xi)-t^xi) - (xi+1) t^(xi+1) + (xi+1) t^(2xi+1)
-# - xi(xi+1) (t^(xi+1)-t^xi) log(t)
-# -(xi+1)(t^(xi+1)-t)-t^2+t^(xi+2)-xi(t^2-t)log(t)
-# +(xi+1)(t^(2xi+1)-t^(xi+1)) +t^(2+xi)-t^(2xi+2)+xi(t^(2+xi)-t^(1+xi))log(t)
-#
-### nach Integration mit Dichte exp(-t) (Gamma bzw Gamma' (bei log) !)
-#
-# -(xi+1)^2 (Gam(2xi+1)-Gam(xi+1)) - (xi+1) Gam(xi+2) + (xi+1) Gam(2xi+2)
-# - xi(xi+1) (Gam'(xi+2)-Gam'(xi+1))
-# -(xi+1)(Gam(xi+2)-Gam(2))-Gam(3)+Gam(xi+3)-xi(Gam'(3)-Gam'(2))
-# +(xi+1)(Gam(2xi+2)-Gam(xi+2))+Gam(3+xi)-Gam(2xi+3)+xi(Gam'(3+xi)-Gam'(2+xi))
-#
-#### ausnutzen Gam(a+1)= a Gam(a)
-# Gam'(a+1) = a Gam'(a) + Gam(a)
-#
-# -(xi+1)^2 (2xi Gam(2xi)- xi Gam(xi)) - (xi+1)^2 xi Gam(xi)
-# + (xi+1)(1+2xi)2xi Gam(2xi)
-# - xi(xi+1) ((1+xi)xi Gam'(xi)+(1+xi)Gam(xi)+xi Gam(xi))
-# + xi(xi+1) (xi Gam'(xi)+ Gam(xi))
-# -(xi+1)((xi+1)xi Gam(xi)- 1)-2+(xi+2)(xi+1)xi Gam(xi)
-# -xi(2Gam'(1)+3-Gam'(1)-1)
-# +(xi+1)((2xi+1)2xi Gam(2xi)-(xi+1)xiGam(xi))+(2+xi)(1+xi)xi Gam(xi)
-# -(2xi+2)(2xi+1)2xi Gam(2xi)
-# +xi((2+xi)(1+xi)xi Gam'(xi)+(2+xi)(1+xi)Gam(xi)+(2+xi)xi Gam(xi)+
-# (1+xi)xiGam(xi)-(1+xi)xiGam'(xi)-(1+xi)Gam(xi)-xi Gam(xi))
-#
-#### ausmultiplizieren
-#
-# -(xi+1)^2 2xi Gam(2xi) +(xi+1)^2 xi Gam(xi) - (xi+1)^2 xi Gam(xi)
-# + (xi+1)(1+2xi)2xi Gam(2xi)
-# - xi(xi+1)(1+xi)xi Gam'(xi)- xi(xi+1)(1+xi)Gam(xi)- xi(xi+1)xi Gam(xi)
-# + xi(xi+1) xi Gam'(xi)+ xi(xi+1) Gam(xi)
-# -(xi+1)(xi+1)xi Gam(xi) +(xi+1)-2+(xi+2)(xi+1)xi Gam(xi)
-# -xi 2 Gam'(1) -3xi +xiGam'(1) +xi
-# +(xi+1)(2xi+1)2xi Gam(2xi)-(xi+1)(xi+1)xiGam(xi)+(2+xi)(1+xi)xi Gam(xi)
-# -(2xi+2)(2xi+1)2xi Gam(2xi)
-# +xi(2+xi)(1+xi)xi Gam'(xi)+xi(2+xi)(1+xi)Gam(xi)+xi(2+xi)xi Gam(xi)+
-# (1+xi)xi^2Gam(xi)-(1+xi)xi^2Gam'(xi)-(1+xi)xiGam(xi)-xi^2 Gam(xi)
-#
-#### Terme sortieren
-#
-# Gam(2xi)[ -(xi+1)^2 2xi + (xi+1)(1+2xi)2xi +(xi+1)(2xi+1)2xi
-# -(2xi+2)(2xi+1)2xi ]
-# Gam(xi)[+(xi+1)^2 xi - (xi+1)^2 xi - xi(xi+1)(1+xi)- xi(xi+1)xi + xi(xi+1)
-# -(xi+1)(xi+1)xi +(xi+2)(xi+1)xi -(xi+1)(xi+1)xi
-# +(2+xi)(1+xi)xi +xi(2+xi)(1+xi)+xi(2+xi)xi +(1+xi)xi^2-(1+xi)xi -xi^2]
-# Gam'(xi)[- xi(xi+1)(1+xi)xi + xi(xi+1) xi +xi(2+xi)(1+xi)xi -(1+xi)xi^2
-# Gam'(1)[ -xi 2 +xi]
-# -3xi+xi+(xi+1)-2
-#
-#### Terme zusammenfassen
-#
-# Gam(2xi)[-2xi^3-4xi^2-2xi + 4xi^3 +6xi^2 +2xi - 4xi^3-6xi^2-2xi]
-# + Gam(xi)[- 2xi^3 - 3xi^2 - xi -xi^2 -2 xi^3 -4xi^2 -2xi + 3x^3+9xi^2+6xi +2xi^2+xi^3+xi^2+xi^3]
-# + Gam'(xi)[xi^2(xi+1)]
-# + Gam'(1)(-xi)
-# - (xi+1)
-#
-# Gam(2xi)[-2xi^3-4xi^2-2xi] + Gam(xi)[ xi^3 +4 xi^2 + 3xi ]
-# + Gam'(xi)[xi^3+xi^2] + Gam'(1)(-xi) - (xi+1)
-#
-#################
-#I22 * xi^4
-#################
-#
-#[(1+xi) (t^xi-1) +t -t^(xi+1) + xi (t-1) log(t)]^2
-#= [(1+xi)^2 (t^xi-1)^2 +t^2 +t^(2xi+2) + xi^2(t-1)^2 log(t)^2 +
-# 2t (1+xi) (t^xi-1) -2 (1+xi)t^(xi+1)(t^xi-1) +2(1+xi)xi(t-1)(t^xi-1)log
-# -2t^(xi+2) +2xi t(t-1)log -2xi t^(xi+1)(t-1)log]^2
-#= [umordnen
-#[(1+xi)^2 (t^xi-1)^2 +t^2 +t^(2xi+2) + 2t (1+xi) (t^xi-1) -2 (1+xi)t^(xi+1)(t^xi-1) -2t^(xi+2)
-# + 2xi(t-1)((1+xi)(t^xi-1)+t -t^(xi+1))log + xi^2(t-1)^2 log(t)^2 ]^2
-#= [ausmultiplizieren]
-#[(1+xi)^2 (t^2xi-2t^xi+1) +t^2 +t^(2xi+2) + 2 (1+xi) (t^(xi+1)-t) -2 (1+xi)(t^(2xi+1)-t^(xi+1)) -2t^(xi+2)
-# + 2xi((1+xi)(t^(xi+1)-t^xi-t+1)+t^2-t -t^(xi+2)+t^(xi+1))log
-# + xi^2(t^2-2t+1) log(t)^2
-#
-#[(1+xi)^2 t^(2xi)-2(1+xi)^2 t^xi + (1+xi)^2 +t^2 + t^(2xi+2) + 2 (1+xi)t^(xi+1)
-# -2(1+xi) t -2 (1+xi) t^(2xi+1) + 2 (1+xi)t^(xi+1) -2 t^(xi+2)]
-# + {2xi(1+xi)t^(xi+1)- 2xi (1+xi) t^xi - 2xi (1+xi) t+ 2xi (1+xi) +2xi t^2 -2xi t
-# -2xi t^(xi+2)}log + xi^2(t^2-2t+1) log(t)^2
-#
-### nach Integration mit Dichte exp(-t)
-# (Gamma bzw Gamma' bzw Gamma'' (bei log, log^2) !)
-#
-#[(1+xi)^2 Gam(2xi+1)-2(1+xi)^2 Gam(xi+1) + (1+xi)^2 +Gam(3) + Gam(2xi+3) + 2 (1+xi)Gam(xi+2)
-# -2(1+xi) Gam(2) -2 (1+xi) Gam(2xi+2) + 2 (1+xi)Gam(xi+2) -2 Gam(xi+3)]
-# + {2xi(1+xi)Gam'(xi+2)- 2xi (1+xi) Gam'(xi+1) - 2xi (1+xi) Gam'(2)+ 2xi (1+xi) Gam'(1)+2xi Gam'(3) -2xi Gam'(2)
-# -2xi Gam'(xi+3)+2xiGam'(xi)} + xi^2(Gam''(3)-2Gam''(2)+Gam''(1))
-#
-#### ausnutzen Gam(a+1)= a Gam(a)
-# Gam'(a+1) = a Gam'(a) + Gam(a)
-# Gam''(a+1) = a Gam'(a) + 2Gam'(a)
-#
-#[(1+xi)^2 2xi Gam(2xi)-2(1+xi)^2 xi Gam(xi) + (1+xi)^2 + 2 +
-# (2xi+2)(2xi+1)2xiGam(2xi) + 2 (1+xi)^2xiGam(xi)
-# -2(1+xi) -2 (1+xi)(1+2xi)2xi Gam(2xi) + 2 (1+xi)^2xi Gam(xi) -2(2+xi)(1+xi)xi Gam(xi)]
-# + {2xi^2(1+xi)^2 Gam'(xi)+2xi(1+xi)^2 Gam(xi)+2xi^2(1+xi)Gam(xi)-
-# - 2xi^2 (1+xi) Gam'(xi) -2xi (1+xi)Gam(xi) - 2xi (1+xi) [Gam'(1)+1]+
-# + 2xi (1+xi) Gam'(1)+2xi [2Gam'(1)+3] -2xi [Gam'(1)+1]
-# -2xi^2 (2+xi)(1+xi)Gam'(xi)-(2+xi)2xi(1+xi) Gam(xi)-2xi^2(xi+2)Gam(xi)-2(1+xi)xi^2 Gam(xi)
-# +2*xi^2(xi+1)Gam'(xi)+2xi(xi+1)Gam(xi)+2xi^2Gam(xi)}
-# + xi^2(2 Gam''(1)+4 Gam'(1)+2 Gam'(1)+2 - 2 Gam''(1)-4Gam'(1)+Gam''(1))
-#
-#### Terme sortieren
-#
-# Gam(2xi)[(1+xi)^2 2xi + (2xi+2)(2xi+1)2xi-2 (1+xi)(1+2xi)2xi]
-#+Gam(xi)[-2(1+xi)^2 xi+ 2(1+xi)^2xi + 2(1+xi)^2xi +2xi(1+xi)^2-2(2+xi)(1+xi)xi
-# +2xi^2(1+xi)-2xi (1+xi) -(2+xi)2xi(1+xi) -2xi^2(xi+2)-
-# -2xi^2(1+xi)+2xi(xi+1)+2xi^2]
-#+Gam'(xi)[2xi^2(1+xi)^2 - 2xi^2 (1+xi) -2xi^2 (2+xi)(1+xi) +2*xi^2(xi+1)]
-#+Gam'(1) [- 2xi (1+xi) + 2xi (1+xi) + 4xi -2xi +4xi^2+2xi^2-4xi^2]
-#+Gam''(1)[2 xi^2 - 2xi^2+xi^2]
-#+ 1 + 2xi + xi^2 + 2 -2(1+xi) - 2xi (1+xi) +6xi -2xi + 2 xi^2
-#
-#### Terme zusammenfassen
-#
-# Gam(2xi)(1+xi)^2 2xi- Gam(xi)2xi((1+xi)^2+1+xi)
-# -Gam'(xi)2xi^2(1+xi)+Gam'(1)2xi(xi+1)+Gam''(1) xi^2 + (1+xi)^2
-#
-### insgesamt
-#
-#################
-#I11 * beta^2 xi^2
-#################
-#
-#2xi(xi+1)^2 Gam(2xi) -[2xi(xi+1)]Gam(xi) + 1
-#
-#################
-#I12 * beta xi^3
-#################
-#
-# - Gam(2xi)2xi(xi+1)^2 + Gam(xi)(xi+1)xi (xi+3)
-# + Gam'(xi)xi^2(xi+1) + Gam'(1)(-xi) - (xi+1)
-#
-#################
-#I22 * xi^4
-#################
-#
-# Gam(2xi)(1+xi)^2 2xi- Gam(xi)2xi(1+xi)(2+xi)
-# -Gam'(xi)2xi^2(1+xi)+Gam'(1)2xi(xi+1)+Gam''(1) xi^2 + (1+xi)^2
-#
-# function(xi,beta){
-# G20 <- gamma(2*xi)
-# G10 <- gamma(xi)
-# G11 <- digamma(xi)*gamma(xi)
-# G01 <- digamma(1)
-# G02 <- trigamma(1)+digamma(1)^2
-# x0 <- 2*xi*(xi+1)^2
-# I11 <- G20*x0-2*G10*xi*(xi+1)+1
-# I11 <- I11/beta^2/xi^2
-# I12 <- G20*(-x0)+ G10*(xi^3+4*xi^2+3*xi) - xi -1
-# I12 <- I12 + G11*(xi^3+xi^2) -G01*xi
-# I12 <- I12/beta/xi^3
-# I22 <- G20*x0 +(xi+1)^2 -G10*(x0+2*xi*(xi+1))
-# I22 <- I22 - G11*2*xi^2*(xi+1) + G01*2*xi*(1+xi)+xi^2 *G02
-# I22 <- I22 /xi^4
-# mat <- PosSemDefSymmMatrix(matrix(c(I11,I12,I12,I22),2,2))
-#
-#}
-
Copied: branches/robast-0.9/pkg/RobExtremes/inst/AddMaterial/comment.txt (from rev 548, branches/robast-0.9/pkg/RobExtremes/R/comment.txt)
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/inst/AddMaterial/comment.txt (rev 0)
+++ branches/robast-0.9/pkg/RobExtremes/inst/AddMaterial/comment.txt 2013-01-23 15:17:13 UTC (rev 549)
@@ -0,0 +1,303 @@
+#
+# Herleitung Expected Shortfall GPD
+# a= 1-p, s=shape; scale= 1
+#q=(a^-s-1)/s
+#VaR + E(X-V|X>V)
+#q + int (X-V)_+ dP/P(X>V) = q + int (V<t) 1-P(t) dt /a=
+# [t=((-loq u)^(-s)-1)/s=(-loq u)^(-s-1)/u]
+#q+ int (V<t) 1-exp(-(1+st)^(-1/s)) dt/a =
+#q+ int_a^1 (-loq (1-u))^(-s) du/a/s = [u=e^-v]
+#q+ int_(1-a) (-loq u)^(-s-1) du/a =
+#q+ int_-log(1-a) v^(-s-1) e^-v du/a = [-logu =v]
+#(a^-s-1)/s+ (1+s(a^-s-1)/s)^(-1/s+1)/(1-s)/a=
+#(a^(-s)-1)/s+ a^(1-s)/(1-s)/a=
+#= q + s (a^(-s)-1)/s/(1-s) + 1/(1-s)=
+#= q + s q/(1-s) + 1/(1-s)=
+#= q/(1-s) + 1/(1-s)
+#
+#=gamma(1-s)/(a*s)*pgamma(-log(a),1-s,lower=F)
+#
+#mit m=loc, b=scale: ES=gamma(1-s)/(a*s)*pgamma(-log(a),1-s,lower=F)*b+m
+#
+# Herleitung L2 Abl GEVD
+## scale component
+## von Nataliya: (kontrolliert: PR)
+## -1/beta-xi*(-1/xi-1)*(x[ind]-mu)/beta^2/(1+xi*(x[ind]-mu)/beta) -
+## (x[ind]-mu)*(1+xi*(x[ind]-mu)/beta)^(-1/xi-1)/beta^2
+# [z=(x[ind]-mu)/beta]
+# = -1/beta-xi*(-1/xi-1)*z/beta/(1+xi*z) - z*(1+xi*z)^(-1/xi-1)/beta
+# = -1/beta+ (xi+1)*z/beta/(1+xi*z) - z*(1+xi*z)^(-1/xi-1)/beta
+# = (-1+ (xi+1)*z/(1+xi*z) - z*(1+xi*z)^(-1/xi-1))/beta
+# = (-(1+xi*z)+ (xi+1)*z - z*(1+xi*z)^(-1/xi))/beta/(1+xi*z)
+# = (-1-xi*z+ xi*z+z - z*(1+xi*z)^(-1/xi))/beta/(1+xi*z)
+# = (-1+z - z*(1+xi*z)^(-1/xi))/beta/(1+xi*z)
+# = (-1+z*(1-(1+xi*z)^(-1/xi)))/beta/(1+xi*z)
+# [zxi = (1+xi*z) ]
+# = (z*(1-zxi^(-1/xi))-1)/beta/zxi
+#
+#
+## shape component
+## von Nataliya: (kontrolliert: PR)
+# log(1+xi*(x[ind]-mu)/beta)/xi^2+(-1/xi-1)*(x[ind]-mu)/beta/
+# (1+xi*(x[ind]-mu)/beta) - (1+xi*(x[ind]-mu)/beta)^(-1/xi)*
+# log(1+xi*(x[ind]-mu)/beta)/xi^2 + (1+xi*(x[ind]-mu)/
+# beta)^(-1/xi-1)*(x[ind]-mu)/beta/xi
+# [z=(x[ind]-mu)/beta]
+# log(1+xi*z)/xi^2+(-1/xi-1)*z/(1+xi*z) - (1+xi*z)^(-1/xi)*
+# log(1+xi*z)/xi^2 + (1+xi*z)^(-1/xi-1)*z/xi
+# [zxi = (1+xi*z) ]
+# log(zxi)/xi^2+(-1/xi-1)*z/(zxi) - (zxi)^(-1/xi)*log(zxi)/xi^2 +
+# (zxi)^(-1/xi-1)*z/xi
+# log(zxi)/xi^2-(1+xi)*z/(zxi)/xi - (zxi)^(-1/xi)*log(zxi)/xi^2 +
+# zxi^(-1/xi-1)*z/xi
+# log(zxi)/xi^2 - (zxi)^(-1/xi)*log(zxi)/xi^2 -(1+xi)*z/(zxi)/xi +
+# zxi^(-1/xi-1)*z/xi
+# log(zxi)/xi^2 * ( 1 - (zxi)^(-1/xi)) +
+# ((zxi)^(-1/xi)-(1+xi))*z/zxi/xi
+# ( 1 - (zxi)^(-1/xi)) * ( log(zxi)/xi^2 - z/zxi/xi) - z/zxi
+# [z/zxi=zu]
+# ( 1 - (zxi)^(-1/xi)) * (log(zxi)/xi - zu)/xi - zu
+
+## umtransformation auf Quantilsskala
+# y = exp(-(1+xi z)^(-1/xi)) <=> -log y = zxi^(-1/xi)
+# <=> (-log y)^(-xi) = zxi <=> z = ((-log y)^(-xi)-1)/xi
+# => zu= z/zxi=((-log y)^(-xi)-1)/xi (-log y)^(xi)
+# =(1-(-log y)^(xi))/xi
+# 1+xi z = zxi = (1-p)^(-xi), z = [(1-p)^(-xi)-1]/xi
+## scale component
+# (z*(1-zxi^(-1/xi))-1)/beta/zxi
+# = (((-log y)^(-xi)-1)/xi*(1-((-log y)^(-xi))^(-1/xi))-1)/beta/
+# ((-log y)^(-xi))
+# = (((-log y)^(-xi)-1)/xi*(1+log y)-1)/beta ((-log y)^(xi))
+# = ((((-log y)^(xi))(-log y)^(-xi)-((-log y)^(xi)))/xi*(1+log y)
+# -((-log y)^(xi)))/beta
+# = ((1-(-log y)^(xi))/xi*(1+log y)-(-log y)^(xi))/beta
+#
+## shape component
+# ( 1 - (zxi)^(-1/xi)) * (log(zxi)/xi - zu)/xi - zu
+# = ( 1 - ((-log y)^(-xi))^(-1/xi)) * (log((-log y)^(-xi))/xi -
+# (1-(-log y)^(xi))/xi)/xi - (1-(-log y)^(xi))/xi
+# = ( 1 + log y) * (-(log(-log y)) - (1-(-log y)^(xi))/xi)/xi -
+# (1-(-log y)^(xi))/xi
+## umtransformation auf Expskala y=exp(-t), t=-log y
+## scale component
+# ((1-(-log y)^(xi))/xi*(1+log y)-(-log y)^(xi))/beta
+# = ((1-t^xi)/xi*(1-t)-t^(xi))/beta
+# = (1-t^xi-t+t^(xi+1)- xi t^xi)/beta/xi
+# = (1-(xi+1) t^xi-t+t^(xi+1))/beta/xi
+#
+## shape component
+# ( 1 + log y) * (-(log(-log y)) - (1-(-log y)^(xi))/xi)/xi -
+# (1-(-log y)^(xi))/xi
+# = ( 1 -t) * (-log(t) - (1-t^xi)/xi)/xi - (1-t^xi)/xi
+# = ( 1 -t) * (- xi log(t) - (1-t^xi))/xi^2 - xi(1-t^xi)/xi^2
+# = [xi(t-1) log(t) + (t-1)(1-t^xi) - xi(1-t^xi)]/xi^2
+# = [xi(t-1) log(t) + t-1-t^(xi+1)+t^xi - xi + xi t^xi)]/xi^2
+# = [xi(t-1) log(t) + t-t^(xi+1)+(1+xi) t^xi - (1+xi))]/xi^2
+
+
+### Integrale bei GEV - FI
+## nach exp(-t) auf 0 .. Inf zu integrieren
+## Lambda = [1-(xi+1)t^xi-t+t^(xi+1)]/(beta xi),
+## [(1+xi) (t^xi-1) +t -t^(xi+1) + xi (t-1) log(t)]/xi^2
+## Lambda Lambda' zu integrieren;
+## dazu int t^a exp(-t) = gamma(a+1),
+## int t^a log(t) exp(-t) = digamma(a+1)
+## int t^a log(t)^2 exp(-t) = trigamma(a+1)
+
+#################
+#I11 * beta^2 xi^2
+#################
+# [1-(xi+1)t^xi-t+t^(xi+1)]^2
+#= [1 + (xi+1)^2 t^(2xi) + t^2 + t^(2xi+2) -
+# -2 (xi+1)t^xi - 2t + 2t^(xi+1)
+# + 2(xi+1)t^(xi+1)-2(xi+1)t^(2xi+1)-2t^(xi+2)]
+#
+### nach Integration mit Dichte exp(-t) (Gamma!)
+#
+#= [1+(xi+1)^2 Gam(2xi+1)+Gam(3)+Gam(2xi+3)-
+# -2(xi+1)Gam(xi+1)-2Gam(2)+2Gam(xi+2)
+# +2(xi+1)Gam(xi+2)-2(xi+1)Gam(2xi+2)-2Gam(xi+3)]
+#
+#### ausnutzen Gam(a+1)= a Gam(a)
+#
+#= 1+2xi(xi+1)^2 Gam(2xi)+2+(2xi+2)(2xi+1)2xi Gam(2xi)-
+# -2(xi+1)xi Gam(xi)-2+ 2(xi+1)xi Gam(xi)
+# +2(xi+1)^2 xi Gam(xi)-2(xi+1)(1+2xi)2xi Gam(2xi)- 2*(xi+2)(xi+1)xi Gam(xi)
+#
+#### Terme sortieren
+#
+#= 1+[2xi(xi+1)^2] Gam(2xi)
+# +[-2(xi+1)xi +2(xi+1)xi +2(xi+1)^2 xi - 2 (xi+2)(xi+1)xi]Gam(xi)
+#
+#### Terme zusammenfassen
+#
+#= 1+[2xi^3-4xi^2-2xi] Gam(2xi)- [2xi^2+2xi]Gam(xi)
+#
+#################
+#I12 * beta xi^3
+#################
+#
+#[1-(xi+1)t^xi-t+t^(xi+1)] [(1+xi) (t^xi-1) +t -t^(xi+1) + xi (t-1) log(t)]
+# = 1 * [...] (=0 weil E Lambda = 0]
+# -(xi+1)^2 (t^(2xi)-t^xi) - (xi+1) t^(xi+1) + (xi+1) t^(2xi+1)
+# - xi(xi+1) (t^(xi+1)-t^xi) log(t)
+# -(xi+1)(t^(xi+1)-t)-t^2+t^(xi+2)-xi(t^2-t)log(t)
+# +(xi+1)(t^(2xi+1)-t^(xi+1)) +t^(2+xi)-t^(2xi+2)+xi(t^(2+xi)-t^(1+xi))log(t)
+#
+### nach Integration mit Dichte exp(-t) (Gamma bzw Gamma' (bei log) !)
+#
+# -(xi+1)^2 (Gam(2xi+1)-Gam(xi+1)) - (xi+1) Gam(xi+2) + (xi+1) Gam(2xi+2)
+# - xi(xi+1) (Gam'(xi+2)-Gam'(xi+1))
+# -(xi+1)(Gam(xi+2)-Gam(2))-Gam(3)+Gam(xi+3)-xi(Gam'(3)-Gam'(2))
+# +(xi+1)(Gam(2xi+2)-Gam(xi+2))+Gam(3+xi)-Gam(2xi+3)+xi(Gam'(3+xi)-Gam'(2+xi))
+#
+#### ausnutzen Gam(a+1)= a Gam(a)
+# Gam'(a+1) = a Gam'(a) + Gam(a)
+#
+# -(xi+1)^2 (2xi Gam(2xi)- xi Gam(xi)) - (xi+1)^2 xi Gam(xi)
+# + (xi+1)(1+2xi)2xi Gam(2xi)
+# - xi(xi+1) ((1+xi)xi Gam'(xi)+(1+xi)Gam(xi)+xi Gam(xi))
+# + xi(xi+1) (xi Gam'(xi)+ Gam(xi))
+# -(xi+1)((xi+1)xi Gam(xi)- 1)-2+(xi+2)(xi+1)xi Gam(xi)
+# -xi(2Gam'(1)+3-Gam'(1)-1)
+# +(xi+1)((2xi+1)2xi Gam(2xi)-(xi+1)xiGam(xi))+(2+xi)(1+xi)xi Gam(xi)
+# -(2xi+2)(2xi+1)2xi Gam(2xi)
+# +xi((2+xi)(1+xi)xi Gam'(xi)+(2+xi)(1+xi)Gam(xi)+(2+xi)xi Gam(xi)+
+# (1+xi)xiGam(xi)-(1+xi)xiGam'(xi)-(1+xi)Gam(xi)-xi Gam(xi))
+#
+#### ausmultiplizieren
+#
+# -(xi+1)^2 2xi Gam(2xi) +(xi+1)^2 xi Gam(xi) - (xi+1)^2 xi Gam(xi)
+# + (xi+1)(1+2xi)2xi Gam(2xi)
+# - xi(xi+1)(1+xi)xi Gam'(xi)- xi(xi+1)(1+xi)Gam(xi)- xi(xi+1)xi Gam(xi)
+# + xi(xi+1) xi Gam'(xi)+ xi(xi+1) Gam(xi)
+# -(xi+1)(xi+1)xi Gam(xi) +(xi+1)-2+(xi+2)(xi+1)xi Gam(xi)
+# -xi 2 Gam'(1) -3xi +xiGam'(1) +xi
+# +(xi+1)(2xi+1)2xi Gam(2xi)-(xi+1)(xi+1)xiGam(xi)+(2+xi)(1+xi)xi Gam(xi)
+# -(2xi+2)(2xi+1)2xi Gam(2xi)
+# +xi(2+xi)(1+xi)xi Gam'(xi)+xi(2+xi)(1+xi)Gam(xi)+xi(2+xi)xi Gam(xi)+
+# (1+xi)xi^2Gam(xi)-(1+xi)xi^2Gam'(xi)-(1+xi)xiGam(xi)-xi^2 Gam(xi)
+#
+#### Terme sortieren
+#
+# Gam(2xi)[ -(xi+1)^2 2xi + (xi+1)(1+2xi)2xi +(xi+1)(2xi+1)2xi
+# -(2xi+2)(2xi+1)2xi ]
+# Gam(xi)[+(xi+1)^2 xi - (xi+1)^2 xi - xi(xi+1)(1+xi)- xi(xi+1)xi + xi(xi+1)
+# -(xi+1)(xi+1)xi +(xi+2)(xi+1)xi -(xi+1)(xi+1)xi
+# +(2+xi)(1+xi)xi +xi(2+xi)(1+xi)+xi(2+xi)xi +(1+xi)xi^2-(1+xi)xi -xi^2]
+# Gam'(xi)[- xi(xi+1)(1+xi)xi + xi(xi+1) xi +xi(2+xi)(1+xi)xi -(1+xi)xi^2
+# Gam'(1)[ -xi 2 +xi]
+# -3xi+xi+(xi+1)-2
+#
+#### Terme zusammenfassen
+#
+# Gam(2xi)[-2xi^3-4xi^2-2xi + 4xi^3 +6xi^2 +2xi - 4xi^3-6xi^2-2xi]
+# + Gam(xi)[- 2xi^3 - 3xi^2 - xi -xi^2 -2 xi^3 -4xi^2 -2xi + 3x^3+9xi^2+6xi +2xi^2+xi^3+xi^2+xi^3]
+# + Gam'(xi)[xi^2(xi+1)]
+# + Gam'(1)(-xi)
+# - (xi+1)
+#
+# Gam(2xi)[-2xi^3-4xi^2-2xi] + Gam(xi)[ xi^3 +4 xi^2 + 3xi ]
+# + Gam'(xi)[xi^3+xi^2] + Gam'(1)(-xi) - (xi+1)
+#
+#################
+#I22 * xi^4
+#################
+#
+#[(1+xi) (t^xi-1) +t -t^(xi+1) + xi (t-1) log(t)]^2
+#= [(1+xi)^2 (t^xi-1)^2 +t^2 +t^(2xi+2) + xi^2(t-1)^2 log(t)^2 +
+# 2t (1+xi) (t^xi-1) -2 (1+xi)t^(xi+1)(t^xi-1) +2(1+xi)xi(t-1)(t^xi-1)log
+# -2t^(xi+2) +2xi t(t-1)log -2xi t^(xi+1)(t-1)log]^2
+#= [umordnen
+#[(1+xi)^2 (t^xi-1)^2 +t^2 +t^(2xi+2) + 2t (1+xi) (t^xi-1) -2 (1+xi)t^(xi+1)(t^xi-1) -2t^(xi+2)
+# + 2xi(t-1)((1+xi)(t^xi-1)+t -t^(xi+1))log + xi^2(t-1)^2 log(t)^2 ]^2
+#= [ausmultiplizieren]
+#[(1+xi)^2 (t^2xi-2t^xi+1) +t^2 +t^(2xi+2) + 2 (1+xi) (t^(xi+1)-t) -2 (1+xi)(t^(2xi+1)-t^(xi+1)) -2t^(xi+2)
+# + 2xi((1+xi)(t^(xi+1)-t^xi-t+1)+t^2-t -t^(xi+2)+t^(xi+1))log
+# + xi^2(t^2-2t+1) log(t)^2
+#
+#[(1+xi)^2 t^(2xi)-2(1+xi)^2 t^xi + (1+xi)^2 +t^2 + t^(2xi+2) + 2 (1+xi)t^(xi+1)
+# -2(1+xi) t -2 (1+xi) t^(2xi+1) + 2 (1+xi)t^(xi+1) -2 t^(xi+2)]
+# + {2xi(1+xi)t^(xi+1)- 2xi (1+xi) t^xi - 2xi (1+xi) t+ 2xi (1+xi) +2xi t^2 -2xi t
+# -2xi t^(xi+2)}log + xi^2(t^2-2t+1) log(t)^2
+#
+### nach Integration mit Dichte exp(-t)
+# (Gamma bzw Gamma' bzw Gamma'' (bei log, log^2) !)
+#
+#[(1+xi)^2 Gam(2xi+1)-2(1+xi)^2 Gam(xi+1) + (1+xi)^2 +Gam(3) + Gam(2xi+3) + 2 (1+xi)Gam(xi+2)
+# -2(1+xi) Gam(2) -2 (1+xi) Gam(2xi+2) + 2 (1+xi)Gam(xi+2) -2 Gam(xi+3)]
+# + {2xi(1+xi)Gam'(xi+2)- 2xi (1+xi) Gam'(xi+1) - 2xi (1+xi) Gam'(2)+ 2xi (1+xi) Gam'(1)+2xi Gam'(3) -2xi Gam'(2)
+# -2xi Gam'(xi+3)+2xiGam'(xi)} + xi^2(Gam''(3)-2Gam''(2)+Gam''(1))
+#
+#### ausnutzen Gam(a+1)= a Gam(a)
+# Gam'(a+1) = a Gam'(a) + Gam(a)
+# Gam''(a+1) = a Gam'(a) + 2Gam'(a)
+#
+#[(1+xi)^2 2xi Gam(2xi)-2(1+xi)^2 xi Gam(xi) + (1+xi)^2 + 2 +
+# (2xi+2)(2xi+1)2xiGam(2xi) + 2 (1+xi)^2xiGam(xi)
+# -2(1+xi) -2 (1+xi)(1+2xi)2xi Gam(2xi) + 2 (1+xi)^2xi Gam(xi) -2(2+xi)(1+xi)xi Gam(xi)]
+# + {2xi^2(1+xi)^2 Gam'(xi)+2xi(1+xi)^2 Gam(xi)+2xi^2(1+xi)Gam(xi)-
+# - 2xi^2 (1+xi) Gam'(xi) -2xi (1+xi)Gam(xi) - 2xi (1+xi) [Gam'(1)+1]+
+# + 2xi (1+xi) Gam'(1)+2xi [2Gam'(1)+3] -2xi [Gam'(1)+1]
+# -2xi^2 (2+xi)(1+xi)Gam'(xi)-(2+xi)2xi(1+xi) Gam(xi)-2xi^2(xi+2)Gam(xi)-2(1+xi)xi^2 Gam(xi)
[TRUNCATED]
To get the complete diff run:
svnlook diff /svnroot/robast -r 549
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