bcpe: The Box-Cox Power Exponential Distribution

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

The Box-Cox Power Exponential Distribution

Description

Density, distribution function, quantile function, and random generation for the Box-Cox power exponential distribution with parameters mu, sigma, lambda, and nu.

Usage

dbcpe(x, mu, sigma, lambda, nu, log = FALSE)

pbcpe(q, mu, sigma, lambda, nu, lower.tail = TRUE)

qbcpe(p, mu, sigma, lambda, nu, lower.tail = TRUE)

rbcpe(n, mu, sigma, lambda, nu)

Arguments

x, q	vector of positive quantiles.
mu	vector of strictly positive scale parameters.
sigma	vector of strictly positive relative dispersion parameters.
lambda	vector of real-valued skewness parameters. If lambda = 0, the Box-Cox power exponential distribution reduces to the log-power exponential distribution with parameters mu, sigma, and nu (see lpe).
nu	strictly positive heavy-tailedness parameter.
log	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
p	vector of probabilities.
n	number of random values to return.

Value

dbcpe returns the density, pbcpe gives the distribution function, qbcpe gives the quantile function, and rbcpe generates random observations.

Invalid arguments will result in return value NaN, with an warning.

The length of the result is determined by n for rbcpe, and is the maximum of the lengths of the numerical arguments for the other functions.

Author(s)

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

References

Rigby, R. A., and 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.

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

mu <- 8
sigma <- 1
lambda <- 2
nu <- 4

# Sample generation
x <- rbcpe(10000, mu, sigma, lambda, nu)

# Density
hist(x, prob = TRUE, main = "The Box-Cox Power Exponential Distribution", col = "white")
curve(dbcpe(x, mu, sigma, lambda, nu), add = TRUE, col = 2, lwd = 2)
legend("topleft", "Probability density function", col = 2, lwd = 2, lty = 1)

# Distribution function
plot(ecdf(x), main = "The Box-Cox Power Exponential Distribution", ylab = "Distribution function")
curve(pbcpe(x, mu, sigma, lambda, nu), add = TRUE, col = 2, lwd = 2)
legend("topleft", c("Emp. distribution function", "Theo. distribution function"),
  col = c(1, 2), lwd = 2, lty = c(1, 1)
)

# Quantile function
plot(seq(0.01, 0.99, 0.001), quantile(x, seq(0.01, 0.99, 0.001)),
  type = "l",
  xlab = "p", ylab = "Quantile function", main = "The Box-Cox Power Exponential Distribution"
)
curve(qbcpe(x, mu, sigma, lambda, nu), add = TRUE, col = 2, lwd = 2, from = 0, to = 1)
legend("topleft", c("Emp. quantile function", "Theo. quantile function"),
  col = c(1, 2), lwd = 2, lty = c(1, 1)
)

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