MBCSec: Multivariate Box-Cox Symmetric Class of Distributions...

In rdmatheus/mbcsec2: Multivariate Box-Cox Symmetric Distributions Generated From Elliptical Copula

Description

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

Usage

dmbcsec(
  x,
  param,
  P = NULL,
  df = 4,
  copula = c("gaussian", "t", "cauchy", "dexponential"),
  gen = "NO"
)

rmbcsec(
  n,
  param,
  P = NULL,
  d = 2L,
  df = NULL,
  copula = c("gaussian", "t", "cauchy", "dexponential"),
  gen = "NO"
)

## S3 method for class 'mbcsec.data'
print(x, ...)

## S3 method for class 'mbcsec.data'
plot(x, method = c("pearson", "kendall", "spearman"), ...)

Arguments

x	Vector or matrix of non-negative quantiles. If x is a matrix, each row is taken to be a quantile. For methods, x is a "mbcsec.data" object.
param	A list that has as components the vectors of marginal parameters mu, sigma, lambda, and nu. In case the marginal distribution is not indexed by nu, it receives NULL by default.
P	Association matrix. If it is specified with NULL (default), then the identity matrix is used.
df	Degrees of freedom associated with the t copula.
copula	Character; informs which distribution in the class of elliptical distributions should be used to generate the elliptical copula. Currently, the copulas available are: Gaussian ("gaussian"), Student's t ("t"), Cauchy ("cauchy"), and double exponential ("dexponential").
gen	A character or a vector character; specifies the distributions generating the marginal BCS distributions. If all BCS margins are generated by the same generating density, it is sufficient to enter only one character. A table with the current available generating distributions for the BCS class can be seen in BCSgen.
n	Number of random values to return.
d	Dimension of the data to be generated. Argument used only in rmbcsec().
...	Further arguments for other specific methods.
method	A character string passed to the plot method indicating which correlation coefficient is to be computed. One of "pearson" (default), "kendall", or "spearman": can be abbreviated.

Value

dmbcsec returns the evaluated joint density function and rmbcsec returns a "mbcsec.data" object that contains the observations generated and the specifications for the multivariate distribution. More specifically, it returns a list with the following components:

• data: Random observations generated from the multivariate distribution specified via rmbcsec().

• spec: A list with the distribution specifications: marginal parameters (param), association matrix (P), degrees of freedom (df), copula (copula), and generating functions for margins (gen).

Author(s)

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

References

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

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

Examples

## Not run: 
### Sample size and dimension
n <- 500
d <- 3

### Association matrix
P <- matrix(c(1, 0.7, -0.5, 0.7, 1, 0.2, -0.5, 0.2, 1), 3, 3)

### Marginals specifications

# Marginals
gen <- c("NO", "ST", "DE")

# Marginal parameters
param <- list(mu = c(10, 6, 1), sigma = c(0.15, 0.15, 0.1),
              lambda = c(-2, 0, 2), nu = c(NA, 2, NA))

### Copula
copula <- "gaussian"

### Generating observations
y <- rmbcsec(n, param, P, d, copula = copula, gen = gen)

y
plot(y)

## End(Not run)

rdmatheus/mbcsec2 documentation built on March 9, 2021, 7:33 p.m.