RTMBdist (version 0.1.0)

exgauss: Exponentially modified Gaussian distribution

Description

Density, distribution function, quantile function, and random generation for the exponentially modified Gaussian distribution.

Usage

dexgauss(x, mu = 0, sigma = 1, lambda = 1, log = FALSE)
pexgauss(q, mu = 0, sigma = 1, lambda = 1, lower.tail = TRUE, log.p = FALSE)
qexgauss(p, mu = 0, sigma = 1, lambda = 1, lower.tail = TRUE, log.p = FALSE)
rexgauss(n, mu = 0, sigma = 1, lambda = 1)

Value

dexgauss gives the density, pexgauss gives the distribution function, qexgauss gives the quantile function, and rexgauss generates random deviates.

Arguments

x, q

vector of quantiles

mu

mean parameter of the Gaussian part

sigma

standard deviation parameter of the Gaussian part, must be positive.

lambda

rate parameter of the exponential part, must be positive.

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

Details

This implementation of dexgauss and pexgauss allows for automatic differentiation with RTMB. qexgauss and rexgauss are reparameterised imports from gamlss.dist::exGAUS.

If \(X \sim N(\mu, \sigma^2)\) and \(Y \sim \text{Exp}(\lambda)\), then \(Z = X + Y\) follows the exponentially modified Gaussian distribution with parameters \(\mu\), \(\sigma\), and \(\lambda\).

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

x <- rexgauss(1, 1, 2, 2)
d <- dexgauss(x, 1, 2, 2)
p <- pexgauss(x, 1, 2, 2)
q <- qexgauss(p, 1, 2, 2)