lsl: The Log-Slash Distribution

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

The Log-Slash Distribution

Description

Density, distribution function, quantile function, and random generation for the log-slash distribution with parameters mu, sigma, and nu.

Usage

dlsl(x, mu, sigma, nu, log = FALSE, ...)

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

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

rlsl(n, mu, sigma, nu)

Arguments

x, q	vector of positive quantiles.
mu	vector of strictly positive scale parameters.
sigma	vector of strictly positive relative dispersion parameters.
nu	strictly positive heavy-tailedness parameter.
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.

Details

A random variable X has a log-slash distribution with parameter mu and sigma if log(X) follows a slash distribution with location parameter log(mu) and dispersion parameter sigma. It can be showed that mu is the median of X.

Value

dlsl returns the density, plsl gives the distribution function, qlsl gives the quantile function, and rlsl generates random observations.

Invalid arguments will result in return value NaN.

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

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 <- 0.4
nu <- 10

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

# Density
hist(x, prob = TRUE, main = "The Log-Slash Distribution", col = "white")
curve(dlsl(x, mu, sigma, nu), add = TRUE, col = 2, lwd = 2)
legend("topright", "Probability density function", col = 2, lwd = 2, lty = 1)

# Distribution function
plot(ecdf(x), main = "The Log-Slash Distribution", ylab = "Distribution function")
curve(plsl(x, mu, sigma, nu), 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 Log-Slash Distribution"
)
curve(qlsl(x, mu, sigma, 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.