| LIN {RelDists} | R Documentation |
The Lindley family
Description
The function LIN() defines the Lindley distribution with only one parameter
for a gamlss.family object to be used in GAMLSS fitting
using the function gamlss().
Usage
LIN(mu.link = "log")
Arguments
mu.link |
defines the mu.link, with "log" link as the default for the mu parameter. |
Details
The Lindley with parameter mu has density given by
f(x) = \frac{\mu^2}{\mu+1} (1+x) \exp(-\mu x),
for x > 0 and \mu > 0.
Value
Returns a gamlss.family object which can be used to fit a LIN distribution in the gamlss() function.
Author(s)
Freddy Hernandez fhernanb@unal.edu.co
References
Lindley DV (1958). “Fiducial distributions and Bayes' theorem.” Journal of the Royal Statistical Society. Series B (Methodological), 102–107.
Lindley DV (1965). Introduction to probability and statistics: from a Bayesian viewpoint. 2. Inference. CUP Archive.
Examples
# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rLIN(n=200, mu=2)
# Fitting the model
require(gamlss)
mod <- gamlss(y ~ 1, family="LIN")
# Extracting the fitted values for mu
# using the inverse link function
exp(coef(mod, what='mu'))
# Example 2
# Generating random values under some model
n <- 100
x1 <- runif(n=n)
x2 <- runif(n=n)
eta <- 1 + 3 * x1 - 2 * x2
mu <- exp(eta)
y <- rLIN(n=n, mu=mu)
mod <- gamlss(y ~ x1 + x2, family=LIN)
coef(mod, what='mu')