BCSgen: Box-Cox Symmetric Distribution Class Generators

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

Description

Current available generating distributions that can be used to fit a model belonging to the Box-Cox symmetric class of distributions.

Usage

BCSgen(dist)

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

Arguments

dist	Character specification of the generating distribution, see details.
x	A "BCSgen" object.
...	Further arguments for other specific methods.

Details

There are some distributions available for the density generating function. The following table display their names and their abbreviations to be passed to BCSgen().

Distribution	Abbreviation	Does it have an extra parameter?
Cauchy	"CA"	no
Canonical slash	"CSL"	no
Double exponential (Laplace)	"DE"	no
Logistic	"LO"	no
Normal	"NO"	no
Power exponential	"PE"	yes
Slash	"SL"	yes
Student-t	"ST"	yes

Value

The function BCSgen() returns a list whose components are set of functions referring to the generating function of the Box-Cox symmetric class of distributions. More specifically, returns an "BCSgen" object with the following elements:

• d: Density generating function function(u, nu).

• p: Cumulative distribution function function(q, nu).

• q: Quantile function function(p, nu).

• extraP: Logical; it receives TRUE if the generating distribution has an extra parameter.

• weigh: Weighting function function(z, nu).

• name: Name of the distribution.

The arguments of the returned functions are:

u, q

Vector of positive quantiles.

p

Vector of probabilities.

z

A vector of transformed responses with the generalized Box-Cox transformation.

nu

Extra parameter of the generating distribution, if it does not exist, it receives NULL.

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(3), 321-344.

Examples

## Not run: 
BCSgen("NO")

curve(BCSgen("NO")$d(x^2), xlim = c(-5, 5),
      ylim = c(0, 0.7), ylab = "Density")
curve(BCSgen("CA")$d(x^2), add = TRUE, col = 2)
curve(BCSgen("CSL")$d(x^2), add = TRUE, col = 3)
curve(BCSgen("DE")$d(x^2), add = TRUE, col = 4)
curve(BCSgen("LO")$d(x^2), add = TRUE, col = 6)
legend("topright", c("Cauchy", "Canonical Slash",
                     "Laplace", "Logistic", "Normal"),
        col = c(2:4, 6, 1), lty = 1, bty = "n")

## End(Not run)

rdmatheus/mbcsec documentation built on April 27, 2021, 1:50 p.m.