bcnsm: The Class of the Multivariate Box-Cox Symmetric Distributions...

In rdmatheus/BCNSM: Multivariate Box-Cox Symmetric Distributions Generated by a Normal Scale Mixture Copula

The Class of the Multivariate Box-Cox Symmetric Distributions Generating by a Normal Scale Mixture Copula

Description

These functions provide the joint probability density function and a random generator for the class of the multivariate Box-Cox symmetric distributions generated by a normal scale mixture copula.

Usage

dbcnsm(
  x,
  mu,
  sigma,
  lambda,
  nu = NULL,
  Gamma = diag(ncol(x)),
  copula = c("gaussian", "t", "slash", "hyp"),
  delta = NULL,
  margins = "bcno",
  log = FALSE
)

rbcnsm(
  n,
  mu,
  sigma,
  lambda,
  nu,
  Gamma = diag(ncol(x)),
  copula = c("gaussian", "t", "slash", "hyp"),
  delta = NULL,
  margins = "bcno"
)

Arguments

x	vector or matrix of non-negative quantiles. If x is a matrix, each row is taken to be a quantile.
mu	vector of the marginal scale parameters in (0, infty)^d, where d is the dimension.
sigma	vector of the marginal relative dispersion parameters in (0, infty)^d, where d is the dimension.
lambda	vector of the marginal skewness parameters in R^d, where d is the dimension.
nu	vector of possible extra parameters of the marginal distributions. In the case where no marginal is indexed by nu, it must be specified with NA.
Gamma	the association matrix. It must be a positive-definite correlation matrix, default is diag(ncol(x)) (the so-called non-associative association structure).
copula	character; informs which normal scale mixture distribution should be used to generate the NSM copula. Currently, the copulas available are: Gaussian ("gaussian"), Student's t ("t"), slash ("slash"), and hyperbolic ("hyp").
delta	possible extra parameter associated with the mixing distribution of the copula. For example, the degrees of freedom of the t copula, or the heavy tailness parameter of the slash or the hyperbolic copula.
margins	a character or a character vector; specifies the marginal BCS distributions. If all BCS margins are the same, it is sufficient to enter only one character. A table with the current available BCS distributions can be seen in bcs.
log	logical; if TRUE, probabilities p are given as log(p).
n	number of replicates to return.

Value

dbcnsm returns the evaluated joint density function and rbcnsm generates random values.

Author(s)

Rodrigo M. R. Medeiros <[e-mail]>

References

Vanegas, L. H., and Paula, G. A. (2016). Log-symmetric distributions: statistical properties and parameter estimation. Brazilian Journal of Probability and Statistics, 30, 196–220.

Ferrari, S. L. P., and Fumes, G. (2017). Box-Cox symmetric distributions and applications to nutritional data. AStA Advances in Statistical Analysis, 101, 321–344.

Examples

### Sample size and dimension
n <- 1000
d <- 4

### Association matrix
Gamma <- matrix(0.8, d, d)
diag(Gamma) <- 1

### Marginal specifications

# Marginals
margins <- c("bchp", "bcsl", "bcpe", "bcloii")

# Marginal parameters
mu <- c(19, 20, 15, 20)
sigma <- c(0.2, 0.6, 0.4, 0.3)
lambda <- c(-1, 1.2, 0, 1.6)
nu <- c(6, 4, 8, NA)

### Copula
copula <- "slash"
delta <- 3

### Generating observations
y <- rbcnsm(n, mu, sigma, lambda, nu, Gamma, copula, delta, margins)

mvplot(y)  ## See ?mvplot for documentation

rdmatheus/BCNSM documentation built on Feb. 8, 2024, 1:28 a.m.