subcopem {subcopem2D} | R Documentation |
Bivariate Empirical Subcopula
Description
Calculation of bivariate empirical subcopula matrix, induced partitions, standardized bivariate sample, and dependence measures for a given bivariate sample.
Usage
subcopem(mat.xy, display = FALSE)
Arguments
mat.xy |
2-column matrix with bivariate observations of a random vector |
display |
logical value indicating if graphs and dependence measures should be displayed. |
Details
Each of the random variables and
may be of any kind (discrete, continuous, or mixed). NA values are not allowed.
Value
A list containing the following components:
depMon |
monotone standardized supremum distance in |
depMonNonSTD |
monotone non-standardized supremum distance |
depSup |
standardized supremum distance in |
depSupNonSTD |
non-standardized supremum distance |
matrix |
matrix with empirical subcopula values. |
part1 |
vector with partition induced by first variable |
part2 |
vector with partition induced by second variable |
sample.size |
numeric value of sample size. |
std.sample |
2-column matrix with the standardized bivariate sample. |
sample |
2-column matrix with the original bivariate sample of |
If display = TRUE
then the values of depMon
, depMonNonSTD
, depSup
, and depSupNonSTD
will be displayed, and the following graphs will be generated: marginal histograms of and
, scatterplots of the original and the standardized bivariate sample, contour and image bivariate graphs of the empirical subcopula.
Note
If both and
are continuous random variables it is faster and better to use
subcopemc
.
Author(s)
Arturo Erdely https://sites.google.com/site/arturoerdely
References
Durante, F. and Sempi, C. (2016) Principles of Copula Theory. Taylor and Francis Group, Boca Raton.
Erdely, A. (2017) A subcopula based dependence measure. Kybernetika 53(2), 231-243. DOI: 10.14736/kyb-2017-2-0231
Nelsen, R.B. (2006) An Introduction to Copulas. Springer, New York.
See Also
Examples
## Example 1: Discrete-discrete Poisson positive dependence
n <- 1000 # sample size
X <- rpois(n, 5) # Poisson(parameter = 5)
p <- 2 # another parameter
Y <- mapply(rpois, rep(1, n), 1 + p*X) # creating dependence
XY <- cbind(X, Y) # 2-column matrix with bivariate sample
cor(XY, method = "pearson")[1, 2] # Pearson's correlation
cor(XY, method = "spearman")[1, 2] # Spearman's correlation
cor(XY, method = "kendall")[1, 2] # Kendall's correlation
SC <- subcopem(XY, display = TRUE)
str(SC)
## Example 2: Continuous-discrete non-monotone dependence
n <- 1000 # sample size
X <- rnorm(n) # Normal(0,1)
Y <- 2*(X > 1) - 1*(X > -1) # Discrete({-1, 0, 1})
XY <- cbind(X, Y) # 2-column matrix with bivariate sample
cor(XY, method = "pearson")[1, 2] # Pearson's correlation
cor(XY, method = "spearman")[1, 2] # Spearman's correlation
cor(XY, method = "kendall")[1, 2] # Kendall's correlation
SC <- subcopem(XY, display = TRUE)
str(SC)