Exponentially modified Gaussian distribution
exgauss.RdDensity, 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)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 \(P[X <= x]\), otherwise, \(P[X > x]\).- p
vector of probabilities
- n
number of random values to return
Value
dexgauss gives the density, pexgauss gives the distribution function, qexgauss gives the quantile function, and rexgauss generates random deviates.
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 \(\lambda\).