# L-comoment Ratio Diagrams for 2- and 3-Parameter Gumbel--Hougaard Extreme Value Copula L-comoment ratio diagrams by computation example are shown for the 2- and 3-parameter **Gumbel--Hougaard copula** (`GHcop`). utf8 ## Author(s) W.H. Asquith ## See Also `lcomCOP` ## Examples ```r ## Not run: # ------------------------------------------------------------------------------------ plot(c(0, 1), c(-0.2, +0.3), type="n", xaxs="i", yaxs="i", xlab="Spearman Rho", ylab="L-coskew or L-cokurtosis") legend("topright", c("L-coskew of GHcop(para=c(b1,b2))", "L-cokurtosis of GHcop(para=c(b1,b2))", "L-coskew of GHcop(para=c(b1,p2,p3))", "L-cokurtosis of GHcop(para=c(b1,p2,p3))"), bty="n", pch=c(15,16,3,4), pt.cex=0.5, col=c("seagreen4", "orchid3", "brown3", "blue3")) fileGH2 <- tempfile(); fileGH3 <- tempfile() nsim <- 10000 for(i in seq_len(nsim)) { if(length(grep("000$", as.character(i)))) message(i,"-", appendLF=FALSE) b1 <- exp(runif(1, min=-6, max=5))+1 # used for both 2- and 3-parameter b2 <- ifelse(length(grep("[13579]$", as.character(i))), # 1/2 between 0..1 and exp(runif(1, min=0, max=5)), runif(1, min=0, max=1)) # 1/2 > 1 t <- b1; p2 <- runif(1, min=0, max=1); p3 <- runif(1, min=0, max=1) GH2 <- lcomCOP(cop=GHcop, para=c(b1, b2), stop.on.error=FALSE) GH3 <- lcomCOP(cop=GHcop, para=c(b1, p2, p3), stop.on.error=FALSE) GH2$lcomUV <- round(GH2$lcomUV, digits=8) GH2$lcomVU <- round(GH2$lcomVU, digits=8) GH3$lcomUV <- round(GH3$lcomUV, digits=8) GH3$lcomVU <- round(GH3$lcomVU, digits=8) d2 <- data.frame(b1, b2, GH2T2.12=GH2$lcomUV[2], GH2T3.12=GH2$lcomUV[3], GH2T4.12=GH2$lcomUV[4], GH2T2.21=GH2$lcomVU[2], GH2T3.21=GH2$lcomVU[3], GH2T4.21=GH2$lcomVU[4]) d3 <- data.frame(b1, p2, p3, GH3T2.12=GH3$lcomUV[2], GH3T3.12=GH3$lcomUV[3], GH3T4.12=GH3$lcomUV[4], GH3T2.21=GH3$lcomVU[2], GH3T3.21=GH3$lcomVU[3], GH3T4.21=GH3$lcomVU[4]) row.names(d2) <- row.names(d3) <- NULL #print(d2); print(d3) if(abs(d2$GH2T2.12) < 1 & d2$GH2T2.12 > 0) { points(d2$GH2T2.12, d2$GH2T3.12, cex=0.5, pch=15, col="seagreen4") points(d2$GH2T2.12, d2$GH2T4.12, cex=0.5, pch=16, col="orchid3" ) } if(abs(d2$GH2T2.21) < 1 & d2$GH2T2.21 > 0) { points(d2$GH2T2.21, d2$GH2T3.21, cex=0.5, pch=15, col="seagreen4") points(d2$GH2T2.21, d2$GH2T4.21, cex=0.5, pch=16, col="orchid3" ) } if(abs(d3$GH3T2.12) < 1 & d3$GH3T2.12 > 0) { points(d3$GH3T2.12, d3$GH3T3.12, cex=0.5, pch= 3, col="brown3") points(d3$GH3T2.12, d3$GH3T4.12, cex=0.5, pch= 4, col="blue3" ) } if(abs(d3$GH3T2.21) < 1 & d3$GH3T2.21 > 0) { points(d3$GH3T2.21, d3$GH3T3.21, cex=0.5, pch= 3, col="brown3") points(d3$GH3T2.21, d3$GH3T4.21, cex=0.5, pch= 4, col="blue3" ) } k <- i == 1 # triggering mechanism for write.table() write.table(d2, file=fileGH2, sep="\t", append=! k, col.names=k, row.names=FALSE) write.table(d3, file=fileGH3, sep="\t", append=! k, col.names=k, row.names=FALSE) } message("done", appendLF=FALSE) fGH2 <- read.table(fileGH2, sep="\t", header=TRUE) fGH3 <- read.table(fileGH3, sep="\t", header=TRUE) # feather::write_feather(fGH2, "LCMrawGH2.feather") # feather::write_feather(fGH3, "LCMrawGH3.feather") # ------------------------------------------------------------------------------------ ## End(Not run) ```

LCOMDIA_GHcop function