empiricalCDF2Dcounts: Computes the empirical bivariate distribution and store the...

In mathphysmx/empiricalDistribution: Empirical Distributions

Description

Computes the matrix of counts for the empirical distribution. To get the real empirical distribution values divede the result by $n$. This function considers that there are no duplicated values both in $x$ and in $y$.

Usage

empiricalCDF2Dcounts(x)

Arguments

x	A 2-columns data.frame with numeric observations (x1,y1),...,(xn,yn).

Details

x[i+1,j+1] is equivalent to Cn(i/n,j/n). Deheuvels, 1979 or Nelsen, 2006.

Value

An integer (n+1)x(n+1)-matrix with the values of the empirical copula multiplied by $n$.

Author(s)

Francisco Mendoza-Torres ([e-mail]) and Arturo Erdely ([e-mail])

References

Equation (3) of Erdely, A. and Diaz-Viera, M. 2010.

Examples

# Example 1
library(squash)
exy <- cbind(1:5, c(2, 4, 3, 6, 7)); print(exy)
set.seed(1); exy <- exy[sample(1:5), ]
print(empiricalCDF2Dcounts(exy))
# to compute the empirical distribution values divide by n
(1/5)* empiricalCDF2Dcounts(exy)

# Example 2
x <- cbind(1:5, c(4, 2, 1, 5, 3))
print(empiricalCDF2Dcounts(x))
# to compute the empirical distribution values divide by n
(1/5)* empiricalCDF2Dcounts(x)

# Example 3 (Error catch):
exy <- cbind(x=c(1:3,2),y=c(1,2,3,2))
# empiricalCDF2Dcounts(exy)

mathphysmx/empiricalDistribution documentation built on May 7, 2019, 10:55 p.m.