Laplace distribution

Density, distribution function, quantile function, and random generation for the Laplace distribution.

Usage

dlaplace(x, mu = 0, b = 1, eps = NULL, log = FALSE)

plaplace(q, mu = 0, b = 1, lower.tail = TRUE, log.p = FALSE)

qlaplace(p, mu = 0, b = 1, lower.tail = TRUE, log.p = FALSE)

rlaplace(n, mu = 0, b = 1)

Arguments

x, q

vector of quantiles

mu

location parameter

b

scale parameter, must be positive.

eps

optional smoothing parameter for dlaplace to smooth the absolute value function. See abs_smooth for details. It is recommended to set this to a small constant like 1e-6 for numerical optimisation.

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

p

vector of probabilities

n

number of random values to return

Value

dlaplace gives the density, plaplace gives the distribution function, qlaplace gives the quantile function, and rlaplace generates random deviates.

Details

This implementation of dlaplace allows for automatic differentiation with RTMB.

Examples

x <- rlaplace(1, 1, 1)
d <- dlaplace(x, 1, 1)
p <- plaplace(x, 1, 1)
q <- qlaplace(p, 1, 1)