Playing with Basic Copula

> library(scatterplot3d)

> x <- seq(0, 1, 0.01)
> y <- seq(0, 1, 0.01)
> z <- (2 * x - 1) * (2 * y - 1)
> scatterplot3d(x, y, z, color = "blue", pch = 19)

> par(mfrow = c(1, 1))
> n <- 10000
> x <- runif(n)
> y <- runif(n)
> z.max <- pmin(x, y)
> z.min <- pmax(x + y - 1, 0)
> scatterplot3d(x, y, z.max, pch = 16, angle = 120, col.grid = "lightblue",
+     highlight.3d = T, col.axis = "blue", main = "Frechet-Hoeffding Lower Bound")

> par(mfrow = c(1, 1))
> n <- 10000
> x <- runif(n)
> y <- runif(n)
> z.max <- pmin(x, y)
> z.min <- pmax(x + y - 1, 0)
> scatterplot3d(x, y, z.max, pch = 16, angle = 120, col.grid = "lightblue",
+     highlight.3d = T, col.axis = "blue", main = "Frechet-Hoeffding Upper Bound")

> par(mfrow = c(1, 1))
> n <- 10000
> x <- runif(n)
> y <- runif(n)
> z <- (x * y)
> scatterplot3d(x, y, z.max, pch = 16, angle = 120, col.grid = "lightblue",
+     highlight.3d = T, col.axis = "blue", main = "Product Copula")