[Robast-commits] r539 - branches/robast-0.9/pkg/RobExtremes/R
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Thu Jan 17 14:35:34 CET 2013
Author: dashunka
Date: 2013-01-17 14:35:34 +0100 (Thu, 17 Jan 2013)
New Revision: 539
Modified:
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/PickandsEstimator.R
Log:
die Kleinigkeiten korrigiert
Modified: branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R 2013-01-17 00:41:38 UTC (rev 538)
+++ branches/robast-0.9/pkg/RobExtremes/R/GEVFamily.R 2013-01-17 13:35:34 UTC (rev 539)
@@ -1,358 +1,357 @@
-#################################
-##
-## Class: GEVFamily for positive shape
-##
-################################
-
-## class
-setClass("GEVFamily", contains="L2ParamFamily")
-
-## methods
-setMethod("validParameter",signature(object="GEVFamily"),
- function(object, param, tol =.Machine$double.eps){
- if (is(param, "ParamFamParameter"))
- param <- main(param)
- if (!all(is.finite(param)))
- return(FALSE)
- if (any(param[1] <= tol))
- return(FALSE)
- if (any(param[2] <= tol))
- return(FALSE)
- return(TRUE)
- })
-
-
-## generating function
-## loc: known/fixed threshold/location parameter
-## scale: scale parameter
-## shape: shape parameter
-## trafo: optional parameter transformation
-## start0Est: startEstimator for MLE and MDE --- if NULL HybridEstimator is used;
-
-GEVFamily <- function(loc = 0, scale = 1, shape = 0.5,
- of.interest = c("scale", "shape"),
- p = NULL, N = NULL, trafo = NULL,
- start0Est = NULL, withPos = TRUE){
- if(is.null(trafo)){
- of.interest <- unique(of.interest)
- if(length(of.interest) > 2)
- stop("A maximum number of two parameters resp. parameter transformations may be selected.")
- if(!all(of.interest %in% c("scale", "shape", "quantile", "expected loss", "expected shortfall")))
- stop("Parameters resp. transformations of interest have to be selected from: ",
- "'scale', 'shape', 'quantile', 'expected loss', 'expected shortfall'.")
-
- ## reordering of of.interest
- if(("scale" %in% of.interest) && ("scale" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "scale"
- }
- if(!("scale" %in% of.interest) && ("shape" %in% of.interest) && ("shape" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "shape"
- }
- if(!any(c("scale", "shape") %in% of.interest) && ("quantile" %in% of.interest)
- && ("quantile" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "quantile"
- }
- if(!any(c("scale", "shape", "quantile") %in% of.interest)
- && ("expected shortfall" %in% of.interest)
- && ("expected shortfall" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "expected shortfall"
- }
- }
- theta <- c(loc, scale, shape)
-
- ##symmetry
- distrSymm <- NoSymmetry()
-
- ## parameters
- names(theta) <- c("loc", "scale", "shape")
-
-
- if(!is.null(p)){
- btq <- substitute({ q <- loc0 + theta[1]*((-log(1-p0))^(-theta[2])-1)/theta[2]
- names(q) <- "quantile"
- }, list(loc0 = loc, p0 = p))
-
- bDq <- substitute({ scale <- theta[1]; shape <- theta[2]
- D1 <- ((-log(1-p0))^(-shape)-1)/shape
- D2 <- -scale/shape*(D1 + log(-log(1-p0))*(-log(1-p0))^(-shape))
- D <- t(c(D1, D2))
- rownames(D) <- "quantile"; colnames(D) <- NULL
- D }, list(p0 = p))
- btes <- substitute({ if(theta[2]>=1L) es <- NA else {
- pg <- pgamma(-log(p0),1-theta[2], lower.tail = FALSE)
- es <- theta[1] * gamma(1-theta[2]) * pg / p0 /
- theta[2] + loc0 }
- names(es) <- "expected shortfall"
- es }, list(loc0 = loc, p0 = p))
- bDes <- substitute({ if(theta[2]>=1L){ D1 <- D2 <- NA} else {
- scale <- theta[1]; shape <- theta[2]
- pg <- pgamma(-log(p0), 1-theta[2], lower.tail = FALSE)
- dd <- ddigamma(-log(p0),1-theta[2])
- D1 <- gamma(1-theta[2])*pg/p0/theta[2]
- D21 <- -theta[1]*gamma(1-theta[2])*pg/p0/theta[2]^2
- D22 < -theta[1]*digamma(1-theta[2])*pg/p0/theta[2]
- D23 <- theta[1]*dd/p0/theta[2]
- D2 <- D21+D22+D23}
- D <- t(c(D1, D2))
- rownames(D) <- "expected shortfall"
- colnames(D) <- NULL
- D }, list(loc0 = loc, p0 = p))
- }
- if(!is.null(N)){
- btel <- substitute({ if(theta[2]>=1L) el <- NA else{
- el <- N0*(loc0+theta[1]*gamma(1-theta[2])/theta[2])}
- names(el) <- "expected loss"
- el }, list(loc0 = loc,N0 = N))
- bDel <- substitute({ if(theta[2]>=1L){ D1 <- D2 <- NA}else{
- scale <- theta[1]; shape <- theta[2]
- D1 <- N0*gamma(1-shape)/shape
- D2 <- -N0*theta[1]*digamma(1-theta[2])/theta[2]-
- D1*scale/(1-shape)}
- D <- t(c(D1, D2))
- rownames(D) <- "expected loss"
- colnames(D) <- NULL
- D }, list(loc0 = loc, N0 = N))
- }
- if(is.null(trafo)){
- tau <- NULL
- if("scale" %in% of.interest){
- tau <- function(theta){ th <- theta[1]; names(th) <- "scale"; th}
- Dtau <- function(theta){ D <- t(c(1, 0)); rownames(D) <- "scale"; D}
- }
- if("shape" %in% of.interest){
- if(is.null(tau)){
- tau <- function(theta){th <- theta[2]; names(th) <- "shape"; th}
- Dtau <- function(theta){D <- t(c(0,1));rownames(D) <- "shape";D}
- }else{
- tau <- function(theta){th <- theta
- names(th) <- c("scale", "shape"); th}
- Dtau <- function(theta){ D <- diag(2);
- rownames(D) <- c("scale", "shape");D}
- }
- }
- }
- if("quantile" %in% of.interest){
- if(is.null(p)) stop("Probability 'p' has to be specified.")
- if(is.null(tau)){
- tau <- function(theta){ }; body(tau) <- btq
- Dtau <- function(theta){ };body(Dtau) <- bDq
- }else{
- tau1 <- tau
- tau <- function(theta){ }
- body(tau) <- substitute({ btq0; c(tau0(theta), q) },
- list(btq0=btq, tau0 = tau1))
- Dtau1 <- Dtau
- Dtau <- function(theta){}
- body(Dtau) <- substitute({ bDq0; rbind(Dtau0(theta), D) },
- list(Dtau0 = Dtau1, bDq0 = bDq))
- }
- }
- if("expected shortfall" %in% of.interest){
- if(is.null(p)) stop("Probability 'p' has to be specified.")
- if(is.null(tau)){
- tau <- function(theta){ }; body(tau) <- btes
- Dtau <- function(theta){ }; body(Dtau) <- bDes
- }else{
- tau1 <- tau
- tau <- function(theta){ }
- body(tau) <- substitute({ btes0; c(tau0(theta), es) },
- list(tau0 = tau1, btes0=btes))
- Dtau1 <- Dtau
- Dtau <- function(theta){}
- body(Dtau) <- substitute({ bDes0; rbind(Dtau0(theta), D) },
- list(Dtau0 = Dtau1, bDes0=bDes))
- }
- }
- if("expected loss" %in% of.interest){
- if(is.null(N)) stop("Expected frequency 'N' has to be specified.")
- if(is.null(tau)){
- tau <- function(theta){ }; body(tau) <- btel
- Dtau <- function(theta){ }; body(Dtau) <- bDel
- }else{
- tau1 <- tau
- tau <- function(theta){ }
- body(tau) <- substitute({ btel0; c(tau0(theta), el) },
- list(tau0 = tau1, btel0=btel))
- Dtau1 <- Dtau
- Dtau <- function(theta){}
- body(Dtau) <- substitute({ bDel0; rbind(Dtau0(theta), D) },
- list(Dtau0 = Dtau1, bDel0=bDel))
- }
- }
- 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")
- }
-
-
- param <- ParamFamParameter(name = "theta", main = c(theta[2],theta[3]),
- fixed = theta[1],
- trafo = trafo, withPosRestr = withPos,
- .returnClsName ="ParamWithScaleAndShapeFamParameter")
-
- ## distribution
- distribution <- GEV(loc = loc, scale = scale, shape = shape)
-
- ## starting parameters
- startPar <- function(x,...){
- mu <- theta[1]
-
- ## Pickand estimator
- if(is.null(start0Est)){
- #source("kMedMad_Qn_Estimators.R")
- e0 <- PickandsEstimator(x,ParamFamily=GParetoFamily(loc = theta[1],
- scale = theta[2], shape = theta[3]))
- }else{
- if(is(start0Est,"function")){
- e1 <- start0Est(x, ...)
- e0 <- if(is(e1,"Estimate")) estimate(e1) else e1
- }
- if(!is.null(names(e0)))
- e0 <- e0[c("scale", "shape")]
- }
- if(any(x < mu-e0["scale"]/e0["shape"]))
- stop("some data smaller than 'loc-scale/shape' ")
-
- names(e0) <- NULL
- return(e0)
- }
-
- ## what to do in case of leaving the parameter domain
- makeOKPar <- function(theta) {
- if(withPos){
- if(!is.null(names(theta)))
- theta["shape"] <- abs(theta["shape"])
- else theta[2] <- abs(theta[2])
- }
- return(theta)
- }
-
- modifyPar <- function(theta){
- theta <- abs(theta)
- GEV(loc = loc, scale = theta[1], shape = theta[2])
- }
-
-
- ## L2-derivative of the distribution
- L2deriv.fct <- function(param) {
- sc <- force(main(param)[1])
- k <- force(main(param)[2])
- tr <- fixed(param)[1]
-
- Lambda1 <- function(x) {
- y <- x*0
- ind <- (x > mu-sc/k) # = [later] (x1>0)
- x <- (x[ind]-tr)/sc
- x1 <- 1 + k * x
- y[ind] <- (x*(1-x1^(-1/k))-1)/x1/sc
-# 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
- return(y)
- }
- Lambda2 <- function(x) {
- y <- x*0
- ind <- (x > tr-sc/k) # = [later] (x1>0)
- x <- (x[ind]-tr)/sc
- x1 <- 1 + k * x
- x2 <- x / x1
- y[ind]<- (1-x1^(-1/k))/k*(log(x1)/k-x2)-x2
-# 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
- return(y)
- }
- ## additional centering of scores to increase numerical precision!
- z1 <- E(distribution, fun=Lambda1)
- z2 <- E(distribution, fun=Lambda2)
- return(list(function(x){ Lambda1(x)-z1 },function(x){ Lambda2(x)-z2 }))
- }
-
- ## Fisher Information matrix as a function of parameters
- FisherInfo.fct <- function(param) {
- sc <- force(main(param)[1])
- k <- force(main(param)[2])
-# tr <- force(fixed(param)[1])
-# fct <- L2deriv.fct(param)
-# P2 <- GPareto(loc = tr, scale = sc, shape = k)
- G20 <- gamma(2*k)
- G10 <- gamma(k)
- G21 <- digamma(2*k)
- G11 <- digamma(k)
- G01 <- digamma(1)
- G02 <- trigamma(1)
- I11 <- G20*2*k*(k^2-4*k+1)+G10*2*k*(k^2+k-1)+1
- I11 <- I11/sc^2/k^2
- I12 <- G20*k*(2*k^2-1)+ G10*k^2*(2-4*k) - k + 3
- I12 <- I12 + G21*2*k^2 -G11*k^2*(k^2+2*k+1) -G01*k
- I12 <- I12/sc/k^3
- I22 <- G20*2*k*(k^2+1)-G10*2*k*(2+3*k+k^2) -3*k^2 +8*k +3
- I22 <- I22 - G11*2*k^2*(1+k)+G10*2*k*(3-k)+k^2 *G02
- I22 <- I22 /k^4
- mat <- PosSemDefSymmMatrix(matrix(c(I11,I12,I12,I22),2,2))
- dimnames(mat) <- list(scaleshapename,scaleshapename)
- return(mat)
- }
-
-
-# FisherInfo.fct <- function(param) {
-# beta <- force(main(param)[1])
-# xi <- force(main(param)[2])
-# mu <- force(fixed(param)[1])
-# fct <- L2deriv.fct(param)
-# P <- GEV(loc = mu, scale = beta, shape = xi)
-# E11 <- E(P,function(x)fct[[1]](x)*fct[[1]](x))
-# E12 <- E(P,function(x)fct[[1]](x)*fct[[2]](x))
-# E22 <- E(P,function(x)fct[[2]](x)*fct[[2]](x))
-# return(PosSemDefSymmMatrix(matrix(c(E11,E12,E12,E22),2,2)))
-# }
-
- FisherInfo <- FisherInfo.fct(param)
- name <- "Generalized Extreme Value Family with positive shape parameter: Frechet Family"
-
- ## initializing the GPareto family with components of L2-family
- L2Fam <- new("GEVFamily")
- L2Fam at scaleshapename <- scaleshapename
- L2Fam at name <- name
- L2Fam at param <- param
- L2Fam at distribution <- distribution
- L2Fam at L2deriv.fct <- L2deriv.fct
- L2Fam at FisherInfo.fct <- FisherInfo.fct
- L2Fam at FisherInfo <- FisherInfo
- L2Fam at startPar <- startPar
- L2Fam at makeOKPar <- makeOKPar
- L2Fam at modifyParam <- modifyPar
- L2Fam at L2derivSymm <- FunSymmList(NonSymmetric(), NonSymmetric())
- L2Fam at L2derivDistrSymm <- DistrSymmList(NoSymmetry(), NoSymmetry())
-
- L2deriv <- EuclRandVarList(RealRandVariable(L2deriv.fct(param),
- Domain = Reals()))
-
- L2Fam at fam.call <- substitute(GEV(loc = loc0, scale = scale0,
- shape = shape0, of.interest = of.interest0,
- p = p0, N = N0, trafo = trafo0,
- withPos = withPos0),
- list(loc0 = loc, scale0 = scale, shape0 = shape,
- of.interest0 = of.interest, p0 = p, N0 = N,
- trafo0 = trafo, withPos0 = withPos))
-
- L2Fam at LogDeriv <- function(x){
- x0 <- (x-loc)/scale
- x1 <- 1 + x0 * shape
- (shape+1)/scale/x1 + x1^(-1-1/shape)/scale
- }
-
- L2Fam at L2deriv <- L2deriv
-
- L2Fam at L2derivDistr <- imageDistr(RandVar = L2deriv, distr = distribution)
-
- return(L2Fam)
-}
-
-#ddigamma(t,s) is d/ds \int_t^\infty exp(-x) (-log(x)) x^(-s) dx
-
-ddigamma <- function(t,s){
- int <- function(x) exp(-x)*(-log(x))*x^(-s)
- integrate(int, lower=t, upper=Inf)$value
- }
+#################################
+##
+## Class: GEVFamily for positive shape
+##
+################################
+
+## class
+setClass("GEVFamily", contains="L2ParamFamily")
+
+## methods
+setMethod("validParameter",signature(object="GEVFamily"),
+ function(object, param, tol =.Machine$double.eps){
+ if (is(param, "ParamFamParameter"))
+ param <- main(param)
+ if (!all(is.finite(param)))
+ return(FALSE)
+ if (any(param[1] <= tol))
+ return(FALSE)
+ if (any(param[2] <= tol))
+ return(FALSE)
+ return(TRUE)
+ })
+
+
+## generating function
+## loc: known/fixed threshold/location parameter
+## scale: scale parameter
+## shape: shape parameter
+## trafo: optional parameter transformation
+## start0Est: startEstimator for MLE and MDE --- if NULL HybridEstimator is used;
+
+GEVFamily <- function(loc = 0, scale = 1, shape = 0.5,
+ of.interest = c("scale", "shape"),
+ p = NULL, N = NULL, trafo = NULL,
+ start0Est = NULL, withPos = TRUE){
+ if(is.null(trafo)){
+ of.interest <- unique(of.interest)
+ if(length(of.interest) > 2)
+ stop("A maximum number of two parameters resp. parameter transformations may be selected.")
+ if(!all(of.interest %in% c("scale", "shape", "quantile", "expected loss", "expected shortfall")))
+ stop("Parameters resp. transformations of interest have to be selected from: ",
+ "'scale', 'shape', 'quantile', 'expected loss', 'expected shortfall'.")
+
+ ## reordering of of.interest
+ if(("scale" %in% of.interest) && ("scale" != of.interest[1])){
+ of.interest[2] <- of.interest[1]
+ of.interest[1] <- "scale"
+ }
+ if(!("scale" %in% of.interest) && ("shape" %in% of.interest) && ("shape" != of.interest[1])){
+ of.interest[2] <- of.interest[1]
+ of.interest[1] <- "shape"
+ }
+ if(!any(c("scale", "shape") %in% of.interest) && ("quantile" %in% of.interest)
+ && ("quantile" != of.interest[1])){
+ of.interest[2] <- of.interest[1]
+ of.interest[1] <- "quantile"
+ }
+ if(!any(c("scale", "shape", "quantile") %in% of.interest)
+ && ("expected shortfall" %in% of.interest)
+ && ("expected shortfall" != of.interest[1])){
+ of.interest[2] <- of.interest[1]
+ of.interest[1] <- "expected shortfall"
+ }
+ }
+ theta <- c(loc, scale, shape)
+
+ ##symmetry
+ distrSymm <- NoSymmetry()
+
+ ## parameters
+ names(theta) <- c("loc", "scale", "shape")
+
+
+ if(!is.null(p)){
+ btq <- substitute({ q <- loc0 + theta[1]*((-log(1-p0))^(-theta[2])-1)/theta[2]
+ names(q) <- "quantile"
+ }, list(loc0 = loc, p0 = p))
+
+ bDq <- substitute({ scale <- theta[1]; shape <- theta[2]
+ D1 <- ((-log(1-p0))^(-shape)-1)/shape
+ D2 <- -scale/shape*(D1 + log(-log(1-p0))*(-log(1-p0))^(-shape))
+ D <- t(c(D1, D2))
+ rownames(D) <- "quantile"; colnames(D) <- NULL
+ D }, list(p0 = p))
+ btes <- substitute({ if(theta[2]>=1L) es <- NA else {
+ pg <- pgamma(-log(p0),1-theta[2], lower.tail = FALSE)
+ es <- theta[1] * gamma(1-theta[2]) * pg / p0 /
+ theta[2] + loc0 }
+ names(es) <- "expected shortfall"
+ es }, list(loc0 = loc, p0 = p))
+ bDes <- substitute({ if(theta[2]>=1L){ D1 <- D2 <- NA} else {
+ scale <- theta[1]; shape <- theta[2]
+ pg <- pgamma(-log(p0), 1-theta[2], lower.tail = FALSE)
+ dd <- ddigamma(-log(p0),1-theta[2])
+ D1 <- gamma(1-theta[2])*pg/p0/theta[2]
+ D21 <- -theta[1]*gamma(1-theta[2])*pg/p0/theta[2]^2
+ D22 < -theta[1]*digamma(1-theta[2])*pg/p0/theta[2]
+ D23 <- theta[1]*dd/p0/theta[2]
+ D2 <- D21+D22+D23}
+ D <- t(c(D1, D2))
+ rownames(D) <- "expected shortfall"
+ colnames(D) <- NULL
+ D }, list(loc0 = loc, p0 = p))
+ }
+ if(!is.null(N)){
+ btel <- substitute({ if(theta[2]>=1L) el <- NA else{
+ el <- N0*(loc0+theta[1]*gamma(1-theta[2])/theta[2])}
+ names(el) <- "expected loss"
+ el }, list(loc0 = loc,N0 = N))
+ bDel <- substitute({ if(theta[2]>=1L){ D1 <- D2 <- NA}else{
+ scale <- theta[1]; shape <- theta[2]
+ D1 <- N0*gamma(1-shape)/shape
+ D2 <- -N0*theta[1]*digamma(1-theta[2])/theta[2]-
+ D1*scale/(1-shape)}
+ D <- t(c(D1, D2))
+ rownames(D) <- "expected loss"
+ colnames(D) <- NULL
+ D }, list(loc0 = loc, N0 = N))
+ }
+ if(is.null(trafo)){
+ tau <- NULL
+ if("scale" %in% of.interest){
+ tau <- function(theta){ th <- theta[1]; names(th) <- "scale"; th}
+ Dtau <- function(theta){ D <- t(c(1, 0)); rownames(D) <- "scale"; D}
+ }
+ if("shape" %in% of.interest){
+ if(is.null(tau)){
+ tau <- function(theta){th <- theta[2]; names(th) <- "shape"; th}
+ Dtau <- function(theta){D <- t(c(0,1));rownames(D) <- "shape";D}
+ }else{
+ tau <- function(theta){th <- theta
+ names(th) <- c("scale", "shape"); th}
+ Dtau <- function(theta){ D <- diag(2);
+ rownames(D) <- c("scale", "shape");D}
+ }
+ }
+ if("quantile" %in% of.interest){
+ if(is.null(p)) stop("Probability 'p' has to be specified.")
+ if(is.null(tau)){
+ tau <- function(theta){ }; body(tau) <- btq
+ Dtau <- function(theta){ };body(Dtau) <- bDq
+ }else{
+ tau1 <- tau
+ tau <- function(theta){ }
+ body(tau) <- substitute({ btq0; c(tau0(theta), q) },
+ list(btq0=btq, tau0 = tau1))
+ Dtau1 <- Dtau
+ Dtau <- function(theta){}
+ body(Dtau) <- substitute({ bDq0; rbind(Dtau0(theta), D) },
+ list(Dtau0 = Dtau1, bDq0 = bDq))
+ }
+ }
+ if("expected shortfall" %in% of.interest){
+ if(is.null(p)) stop("Probability 'p' has to be specified.")
+ if(is.null(tau)){
+ tau <- function(theta){ }; body(tau) <- btes
+ Dtau <- function(theta){ }; body(Dtau) <- bDes
+ }else{
+ tau1 <- tau
+ tau <- function(theta){ }
+ body(tau) <- substitute({ btes0; c(tau0(theta), es) },
+ list(tau0 = tau1, btes0=btes))
+ Dtau1 <- Dtau
+ Dtau <- function(theta){}
+ body(Dtau) <- substitute({ bDes0; rbind(Dtau0(theta), D) },
+ list(Dtau0 = Dtau1, bDes0=bDes))
+ }
+ }
+ if("expected loss" %in% of.interest){
+ if(is.null(N)) stop("Expected frequency 'N' has to be specified.")
+ if(is.null(tau)){
+ tau <- function(theta){ }; body(tau) <- btel
+ Dtau <- function(theta){ }; body(Dtau) <- bDel
+ }else{
+ tau1 <- tau
+ tau <- function(theta){ }
+ body(tau) <- substitute({ btel0; c(tau0(theta), el) },
+ list(tau0 = tau1, btel0=btel))
+ Dtau1 <- Dtau
+ Dtau <- function(theta){}
+ body(Dtau) <- substitute({ bDel0; rbind(Dtau0(theta), D) },
+ list(Dtau0 = Dtau1, bDel0=bDel))
+ }
+ }
+ 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")
+ }
+
+
+ param <- ParamFamParameter(name = "theta", main = c(theta[2],theta[3]),
+ fixed = theta[1],
+ trafo = trafo, withPosRestr = withPos,
+ .returnClsName ="ParamWithScaleAndShapeFamParameter")
+
+ ## distribution
+ distribution <- GEV(loc = loc, scale = scale, shape = shape)
+
+ ## starting parameters
+ startPar <- function(x,...){
+ mu <- theta[1]
+
+ ## Pickand estimator
+ if(is.null(start0Est)){
+ #source("kMedMad_Qn_Estimators.R")
+ e0 <- PickandsEstimator(x,ParamFamily=GParetoFamily(loc = theta[1],
+ scale = theta[2], shape = theta[3]))
+ }else{
+ if(is(start0Est,"function")){
+ e1 <- start0Est(x, ...)
+ e0 <- if(is(e1,"Estimate")) estimate(e1) else e1
+ }
+ if(!is.null(names(e0)))
+ e0 <- e0[c("scale", "shape")]
+ }
+ if(any(x < mu-e0["scale"]/e0["shape"]))
+ stop("some data smaller than 'loc-scale/shape' ")
+
+ names(e0) <- NULL
+ return(e0)
+ }
+
+ ## what to do in case of leaving the parameter domain
+ makeOKPar <- function(theta) {
+ if(withPos){
+ if(!is.null(names(theta)))
+ theta["shape"] <- abs(theta["shape"])
+ else theta[2] <- abs(theta[2])
+ }
+ return(theta)
+ }
+
+ modifyPar <- function(theta){
+ theta <- abs(theta)
+ GEV(loc = loc, scale = theta[1], shape = theta[2])
+ }
+
+
+ ## L2-derivative of the distribution
+ L2deriv.fct <- function(param) {
+ sc <- force(main(param)[1])
+ k <- force(main(param)[2])
+ tr <- fixed(param)[1]
+
+ Lambda1 <- function(x) {
+ y <- x*0
+ ind <- (x > mu-sc/k) # = [later] (x1>0)
+ x <- (x[ind]-tr)/sc
+ x1 <- 1 + k * x
+ y[ind] <- (x*(1-x1^(-1/k))-1)/x1/sc
+# 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
+ return(y)
+ }
+ Lambda2 <- function(x) {
+ y <- x*0
+ ind <- (x > tr-sc/k) # = [later] (x1>0)
+ x <- (x[ind]-tr)/sc
+ x1 <- 1 + k * x
+ x2 <- x / x1
+ y[ind]<- (1-x1^(-1/k))/k*(log(x1)/k-x2)-x2
+# 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
+ return(y)
+ }
+ ## additional centering of scores to increase numerical precision!
+ z1 <- E(distribution, fun=Lambda1)
+ z2 <- E(distribution, fun=Lambda2)
+ return(list(function(x){ Lambda1(x)-z1 },function(x){ Lambda2(x)-z2 }))
+ }
+
+ ## Fisher Information matrix as a function of parameters
+ FisherInfo.fct <- function(param) {
+ sc <- force(main(param)[1])
+ k <- force(main(param)[2])
+# tr <- force(fixed(param)[1])
+# fct <- L2deriv.fct(param)
+# P2 <- GPareto(loc = tr, scale = sc, shape = k)
+ G20 <- gamma(2*k)
+ G10 <- gamma(k)
+ G21 <- digamma(2*k)
+ G11 <- digamma(k)
+ G01 <- digamma(1)
+ G02 <- trigamma(1)
+ I11 <- G20*2*k*(k^2-4*k+1)+G10*2*k*(k^2+k-1)+1
+ I11 <- I11/sc^2/k^2
+ I12 <- G20*k*(2*k^2-1)+ G10*k^2*(2-4*k) - k + 3
+ I12 <- I12 + G21*2*k^2 -G11*k^2*(k^2+2*k+1) -G01*k
+ I12 <- I12/sc/k^3
+ I22 <- G20*2*k*(k^2+1)-G10*2*k*(2+3*k+k^2) -3*k^2 +8*k +3
+ I22 <- I22 - G11*2*k^2*(1+k)+G10*2*k*(3-k)+k^2 *G02
+ I22 <- I22 /k^4
+ mat <- PosSemDefSymmMatrix(matrix(c(I11,I12,I12,I22),2,2))
+ dimnames(mat) <- list(scaleshapename,scaleshapename)
+ return(mat)
+ }
+
+
+# FisherInfo.fct <- function(param) {
+# beta <- force(main(param)[1])
+# xi <- force(main(param)[2])
+# mu <- force(fixed(param)[1])
+# fct <- L2deriv.fct(param)
+# P <- GEV(loc = mu, scale = beta, shape = xi)
+# E11 <- E(P,function(x)fct[[1]](x)*fct[[1]](x))
+# E12 <- E(P,function(x)fct[[1]](x)*fct[[2]](x))
+# E22 <- E(P,function(x)fct[[2]](x)*fct[[2]](x))
+# return(PosSemDefSymmMatrix(matrix(c(E11,E12,E12,E22),2,2)))
+# }
+
+ FisherInfo <- FisherInfo.fct(param)
+ name <- "Generalized Extreme Value Family with positive shape parameter: Frechet Family"
+
+ ## initializing the GPareto family with components of L2-family
+ L2Fam <- new("GEVFamily")
+ L2Fam at scaleshapename <- scaleshapename
+ L2Fam at name <- name
+ L2Fam at param <- param
+ L2Fam at distribution <- distribution
+ L2Fam at L2deriv.fct <- L2deriv.fct
+ L2Fam at FisherInfo.fct <- FisherInfo.fct
+ L2Fam at FisherInfo <- FisherInfo
+ L2Fam at startPar <- startPar
+ L2Fam at makeOKPar <- makeOKPar
+ L2Fam at modifyParam <- modifyPar
+ L2Fam at L2derivSymm <- FunSymmList(NonSymmetric(), NonSymmetric())
+ L2Fam at L2derivDistrSymm <- DistrSymmList(NoSymmetry(), NoSymmetry())
+
+ L2deriv <- EuclRandVarList(RealRandVariable(L2deriv.fct(param),
+ Domain = Reals()))
+
+ L2Fam at fam.call <- substitute(GEV(loc = loc0, scale = scale0,
+ shape = shape0, of.interest = of.interest0,
+ p = p0, N = N0, trafo = trafo0,
+ withPos = withPos0),
+ list(loc0 = loc, scale0 = scale, shape0 = shape,
+ of.interest0 = of.interest, p0 = p, N0 = N,
+ trafo0 = trafo, withPos0 = withPos))
+
+ L2Fam at LogDeriv <- function(x){
+ x0 <- (x-loc)/scale
+ x1 <- 1 + x0 * shape
+ (shape+1)/scale/x1 + x1^(-1-1/shape)/scale
+ }
+
+ L2Fam at L2deriv <- L2deriv
+
+ L2Fam at L2derivDistr <- imageDistr(RandVar = L2deriv, distr = distribution)
+
+ return(L2Fam)
+}
+
+#ddigamma(t,s) is d/ds \int_t^\infty exp(-x) (-log(x)) x^(-s) dx
+
+ddigamma <- function(t,s){
+ int <- function(x) exp(-x)*(-log(x))*x^(-s)
+ integrate(int, lower=t, upper=Inf)$value
+ }
\ No newline at end of file
Modified: branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R
===================================================================
--- branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R 2013-01-17 00:41:38 UTC (rev 538)
+++ branches/robast-0.9/pkg/RobExtremes/R/GParetoFamily.R 2013-01-17 13:35:34 UTC (rev 539)
@@ -1,331 +1,332 @@
-#################################
-##
-## Class: GParetoFamily
-##
-################################
-
-
-## methods
-setMethod("validParameter",signature(object="GParetoFamily"),
- function(object, param, tol =.Machine$double.eps){
- if (is(param, "ParamFamParameter"))
- param <- main(param)
- if (!all(is.finite(param)))
- return(FALSE)
- #if (any(param[1] <= tol))
- # return(FALSE)
- if(object at param@withPosRestr)
- if (any(param[2] <= tol))
- return(FALSE)
- return(TRUE)
- })
-
-
-## generating function
-## loc: known/fixed threshold/location parameter
-## scale: scale parameter
-## shape: shape parameter
-## of.interest: which parameters, transformations are of interest
-## posibilites are: scale, shape, quantile, expected loss, expected shortfall
-## a maximum number of two of these may be selected
-## p: probability needed for quantile and expected shortfall
-## N: expected frequency for expected loss
-## trafo: optional parameter transformation
-## start0Est: startEstimator for MLE and MDE --- if NULL HybridEstimator is used;
-### now uses exp-Trafo for scale!
-
-GParetoFamily <- function(loc = 0, scale = 1, shape = 0.5,
- of.interest = c("scale", "shape"),
- p = NULL, N = NULL, trafo = NULL,
- start0Est = NULL, withPos = TRUE){
- if(is.null(trafo)){
- of.interest <- unique(of.interest)
- if(length(of.interest) > 2)
- stop("A maximum number of two parameters resp. parameter transformations may be selected.")
- if(!all(of.interest %in% c("scale", "shape", "quantile", "expected loss", "expected shortfall")))
- stop("Parameters resp. transformations of interest have to be selected from: ",
- "'scale', 'shape', 'quantile', 'expected loss', 'expected shortfall'.")
-
- ## reordering of of.interest
- if(("scale" %in% of.interest) && ("scale" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "scale"
- }
- if(!("scale" %in% of.interest) && ("shape" %in% of.interest) && ("shape" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "shape"
- }
- if(!any(c("scale", "shape") %in% of.interest) && ("quantile" %in% of.interest)
- && ("quantile" != of.interest[1])){
- of.interest[2] <- of.interest[1]
- of.interest[1] <- "quantile"
- }
- if(!any(c("scale", "shape", "quantile") %in% of.interest)
- && ("expected shortfall" %in% of.interest)
[TRUNCATED]
To get the complete diff run:
svnlook diff /svnroot/robast -r 539
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