uvSim: Bernstein copula simulation of a bivariate uniform...

In mathphysmx/bernstein: Bernstein-bezier curves and surfaces

Description

Bernstein copula simulation of a bivariate uniform distribution. The bivariate uniform distribution can be a transformed one from non-uniform data.

Usage

uvSim(n = 100, diffEC, u = NULL, t = NULL, delta = 0, ...)

Arguments

n	An integer specifying the number of simulations required.
diffEC	Forward difference with respect of $x$ of the empirical copula matrix. Maybe computed with forwardDifference of empiricalCDF2Dcounts. empiricalCDF2Dcounts.
u	non-exceedance probabilities used for conditional simulation. Default to NULL, but if specified, then n = length(u)
t	Numeric value in [0,1] for repreducible research.
delta	numeric. Ideally must be zero, but it is used for numerical computation stability, say, .Machine$double.eps^0.07.
...	further arguments passed to uniroot

Value

a 2-columns matrix of simulated pseudo-observations u,v.

References

Section 2.9 (Random Variate Generation) Nelsen, 2006

Examples

# Common to Examples 1, 2 and 3
en <- 100
library(copBasic)
set.seed(123); eu <- runif(en)
ev <- simCOPv(u = eu, cop=PLACKETTcop, para=20.1, snv=F) # simulate strong positive Plackett
plot.default(eu, ev, asp = 1, xlim = 0:1, ylim = 0:1, main = "data")
library(empiricalDistribution)
empCopulaCountsmatrix <- empiricalCDF2Dcounts(data.frame(U=eu, V=ev))
fDiffEmpCopMatrix <- forwardDifference(empCopulaCountsmatrix)
library(inverseFunction)

# Example 1 (n is given):
evMySim1 <- uvSim(n = en, diffEC = fDiffEmpCopMatrix)
plot.default(evMySim1, asp = 1, xlim = 0:1, ylim = 0:1, main = "Ex1")

# Example 2 (u is given):
evMySim2 <- uvSim(n = en, diffEC = fDiffEmpCopMatrix, u = eu)
plot.default(evMySim2, asp = 1, xlim = 0:1, ylim = 0:1, main = "Ex2")

# Example 3 (Reproducible Research, u and t are given):
et <- evMySim2[, 3]
evMySim3 <- uvSim(n = 100, diffEC = fDiffEmpCopMatrix, u = eu, t = et)
all.equal(evMySim2, evMySim3)
plot.default(evMySim3, asp = 1, xlim = 0:1, ylim = 0:1, main = "Ex3")

mathphysmx/bernstein documentation built on Sept. 3, 2019, 12:57 p.m.