## ----setup, include=FALSE----------------------------------------------------- knitr::opts_chunk$set(cache=TRUE) ## ----------------------------------------------------------------------------- library(copula) # Gaussian copula where correlation is 0.5 gaus_copula <- normalCopula(0.5, dim = 2) sample_copula1 <- rCopula(1000, gaus_copula) plot(sample_copula1) # Compare with independent copula, # i.e. two independent uniform variables. gaus_copula <- normalCopula(0, dim = 2) sample_copula2 <- rCopula(1000, gaus_copula) plot(sample_copula2) ## ----echo = FALSE------------------------------------------------------------- par(mfrow = c(1, 2)) plot(sample_copula1, main = "Corr. 0.5") plot(sample_copula2, main = "Independent") ## ----------------------------------------------------------------------------- # Clayton copula with theta = 0.5 clay_copula <- claytonCopula(param = 0.5) sample_copula1 <- rCopula(1000, clay_copula) plot(sample_copula1) ## ----echo = FALSE, warning = FALSE, message = FALSE--------------------------- clay_copula <- claytonCopula(param = 0) sample_copula1 <- rCopula(1000, clay_copula) clay_copula <- claytonCopula(param = 0.5) sample_copula2 <- rCopula(1000, clay_copula) clay_copula <- claytonCopula(param = 1) sample_copula3 <- rCopula(1000, clay_copula) clay_copula <- claytonCopula(param = 2) sample_copula4 <- rCopula(1000, clay_copula) par(mfrow = c(2, 2)) plot(sample_copula1, main = "Independent") plot(sample_copula2, main = expression(paste(theta, "= 0.5"))) plot(sample_copula3, main = expression(paste(theta, "= 1"))) plot(sample_copula4, main = expression(paste(theta, "= 2"))) ## ----------------------------------------------------------------------------- A <- matrix(c(5, 4, 4, 5), ncol = 2) results <- eigen(A, symmetric = TRUE, only.values = TRUE) c("GV" = prod(results$values), "TV" = sum(results$values)) # Compare this with the following B <- matrix(c(5, -4, -4, 5), ncol = 2) # GV(A) = 9; TV(A) = 10 c("GV" = det(B), "TV" = sum(diag(B)))