dHAC function

pdf, cdf and random sampling

dHAC and pHAC compute the values of the copula's density and cumulative distribution function respectively. rHAC samples from HAC.

dHAC(X, hac, eval = TRUE, margins = NULL, na.rm = FALSE, ...)
pHAC(X, hac, margins = NULL, na.rm = FALSE, ...)
rHAC(n, hac)

Arguments

• X: a data matrix. The number of columns and the corresponding names have to coincide with the specifications of the copula model hac.
• hac: an object of the class hac.
• n: number of observations.
• margins: specifies the margins. The data matrix X is assumed to contain the values of the marginal distributions by default, i.e. margins = NULL. If raw data are used, the margins can be determined nonparametrically, "edf", or in parametric way, e.g. "norm". See estimate.copula for a detailed explanation.
• na.rm: boolean. If na.rm = TRUE, missing values, NA, contained in X are removed.
• eval: boolean. If eval = FALSE, a non-evaluated function is returned. Note, that attr "gradient" of the returned function corresponds to the values density.
• ...: arguments to be passed to na.omit.

Returns

rHAC retruns a $n \times d$ matrix, where $d$ refers to the dimension of the HAC. dHAC and pHAC return vectors. The computation of the density might be time consuming for high-dimensions, since the density is defined as $d$-th derivative of the HAC with respect to its arguments $u_1, \ldots, u_d$.

Details

Sampling schemes of hierarchical and densities of simple Archimedean copula are based on functions of the copula package.

References

Hofert, M. 2011, Efficiently Sampling Nested Archimedean Copulas, Computational Statistics & Data Analysis 55, 57-70.

Joe, H. 1997, Multivariate Models and Dependence Concepts, Chapman & Hall.

McNeil, A. J. 2008, Sampling Nested Archimedean Copulas, Journal of Statistical Computation and Simulation 78, 567-581.

Nelsen, R. B. 2006, An Introduction to Copulas, Spinger, 2nd Edition.

Okhrin, O. and Ristig, A. 2014, Hierarchical Archimedean Copulae: The HAC Package", Journal of Statistical Software, 58(4), 1-20, tools:::Rd_expr_doi("10.18637/jss.v058.i04") .

Savu, C. and Trede, M. 2010, Hierarchies of Archimedean copulas, Quantitative Finance 10, 295-304.

See Also

estimate.copula, to.logLik

Examples

# AC example
# define the underlying model
model = hac(type = 4, tree = list("X1", "X2", 2))

# sample from model
sample = rHAC(100, model)

# returns the pdf/cdf at each vector of the sample
d.values = dHAC(sample, model)
p.values = pHAC(sample, model)

# HAC example
# the underlying model
y = c("X1", "X2", "X3")
theta = c(1.5, 3)
model = hac.full(type = 1, y, theta)

# define sample from copula model
sample = rHAC(100, model)

# returns the pdf/cdf at each point of the sample
d.values = dHAC(sample, model)
p.values = pHAC(sample, model)

# construct a hac-model
tree = list(list("X1", "X5", 3), list("X2", "X3", "X4", 4), 2)
model = hac(type = 1, tree = tree)

# sample from copula model
sample = rHAC(1000, model)

# check the accurancy of the estimation procedure
result1 = estimate.copula(sample)
result2 = estimate.copula(sample, epsilon = 0.2)