bcloii: The Box-Cox Type II Logistic Distribution

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

The Box-Cox Type II Logistic Distribution

Description

Density, distribution function, quantile function, and random generation for the Box-Cox type II logistic distribution with parameters mu, sigma, and lambda.

Usage

dbcloii(x, mu, sigma, lambda, log = FALSE, ...)

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

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

rbcloii(n, mu, sigma, lambda)

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 type II logistic distribution reduces to the log-type II logistic distribution with parameters mu and sigma (see lloii).
log	logical; if TRUE, probabilities p are given as log(p).
...	further arguments.
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

dbcloii returns the density, pbcloii gives the distribution function, qbcloii gives the quantile function, and rbcloii generates random observations.

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

The length of the result is determined by n for rbcloii, 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

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.

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.

Examples

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

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

# Density
hist(x, prob = TRUE, main = "The Box-Cox Type II Logistic Distribution", col = "white")
curve(dbcloii(x, mu, sigma, lambda), add = TRUE, col = 2, lwd = 2)
legend("topright", "Probability density function", col = 2, lwd = 2, lty = 1)

# Distribution function
plot(ecdf(x), main = "The Box-Cox Type II Logistic Distribution", ylab = "Distribution function")
curve(pbcloii(x, mu, sigma, lambda), add = TRUE, col = 2, lwd = 2)
legend("bottomright", 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 Type II Logistic Distribution"
)
curve(qbcloii(x, mu, sigma, lambda), 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.