BCS: The Box-Cox Symmetric Class of Distributions

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

Description

Probability mass function, cumulative distribution function, quantile function, and random generation for the Box-Cox symmetric (BCS) class of distributions.

Usage

dBCS(x, mu, sigma, lambda, nu = NULL, gen = "NO")

pBCS(q, mu, sigma, lambda, nu = NULL, gen = "NO")

qBCS(p, mu, sigma, lambda, nu = NULL, gen = "NO")

rBCS(n, mu, sigma, lambda, nu = NULL, gen = "NO", rep = 1L)

Arguments

x, q	vector of non-negative quantiles.
mu	vector of location parameter values.
sigma	vector of dispersion parameter values.
lambda	vector of skewness parameter values.
nu	vector of right tail/kurtosis parameter values. Not all distributions are indexed by this parameter. In this case, nu = NULL.
gen	character specification passed as argument to BCSgen. It specifies the generating distribution for the BCS class of distributions. A table with the current available generating distributions can be seen in details.
p	vector of probabilities.
n	number of random values to return.
rep	number of replicates with size n to return.

Details

This set of functions represents the probability function, the cumulative distribution function, quantile function, and a random number generator for the Box-Cox symmetric class of distributions proposed by Ferrari and Fumes (2017). This class of distributions includes the Box-Cox t (Rigby and Stasinopoulos, 2006), Box-Cox Cole-Green (or Box-Cox normal; Cole and Green, 1992), Box-Cox power exponential (Rigby and Stasinopoulos, 2004) distributions, and the class of the log-symmetric distributions (Vanegas and Paula, 2016) as special cases. The current available generating distributions can be seen below.

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

dBCS returns the density function, pBCS gives the distribution function, qBCS gives the quantile function, and rBCS generates random observations.

Author(s)

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

References

Cole, T., & Green, P.J. (1992). Smoothing reference centile curves: the LMS method and penalized likelihood. Stat. Med, 11, 1305–1319.

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

Rigby, R. A., & Stasinopoulos, D. M. (2004). Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution. Statistics in medicine, 23, 3053–3076.

Rigby, R. A., & Stasinopoulos, D. M. (2006). Using the Box-Cox t distribution in GAMLSS to model skewness and kurtosis. Statistical Modelling, 6, 209-229.

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: 
## Box-Cox t
y <- rBCS(500, 8, 0.15, 1, 10, gen = "ST")

par(mfrow = c(1, 2))
hist(y, prob = TRUE, main = "Box Cox t")
curve(dBCS(x, 8, 0.15, 1, 10, gen = "ST"), add = TRUE, col = 2, lwd = 2)
plot(ecdf(y), main = "", xlab = "y")
curve(pBCS(x, 8, 0.15, 1, 10, gen = "ST"), add = TRUE, col = 2, lwd = 2)

## Box-Cox Cole-Green
y <- rBCS(500, 8, 0.15, 1, 10, gen = "NO")

hist(y, prob = TRUE, main = "Box Cox Cole-Green")
curve(dBCS(x, 8, 0.15, 1, 10, gen = "NO"), add = TRUE, col = 2, lwd = 2)
plot(ecdf(y), main = "", xlab = "y")
curve(pBCS(x, 8, 0.15, 1, 10, gen = "NO"), add = TRUE, col = 2, lwd = 2)

## Box-Cox Cauchy
y <- rBCS(500, 8, 0.15, -1.2, gen = "CA")

hist(y, prob = TRUE, main = "Box-Cox Cauchy")
curve(dBCS(x, 8, 0.15, -1.2, gen = "CA"), add = TRUE, col = 2, lwd = 2)
plot(ecdf(y), main = "", xlab = "y")
curve(pBCS(x, 8, 0.15, -1.2, gen = "CA"), add = TRUE, col = 2, lwd = 2)

## Box-Cox power exponential
y <- rBCS(500, 8, 0.15, 1, 10, gen = "PE")

hist(y, prob = TRUE, main = "Box Cox PE")
curve(dBCS(x, 8, 0.15, 1, 10, gen = "PE"), add = TRUE, col = 2, lwd = 2)
plot(ecdf(y), main = "")
curve(pBCS(x, 8, 0.15, 1, 10, gen = "PE"), add = TRUE, col = 2, lwd = 2)

## End(Not run)

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