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().
Value
Returns a gamlss.family object which can be used to fit a LIN distribution in the gamlss() function.
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 \(\mu > 0\).
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.
Author
Freddy Hernandez fhernanb@unal.edu.co
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")
#> GAMLSS-RS iteration 1: Global Deviance = 246.8283
# Extracting the fitted values for mu
# using the inverse link function
exp(coef(mod, what='mu'))
#> (Intercept)
#> 1.94916
# 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)
#> GAMLSS-RS iteration 1: Global Deviance = -98.3703
#> GAMLSS-RS iteration 2: Global Deviance = -98.3703
coef(mod, what='mu')
#> (Intercept) x1 x2
#> 1.390277 3.167817 -2.751112