LIN function

The Lindley family

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().

LIN(mu.link = "log")

Arguments

• mu.link: defines the mu.link, with "log" link as the default for the mu parameter.

Returns

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 $\mu > 0$.

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')

References

Rdpack::insert_ref(key="lindley1958fiducial",package="RelDists")

Rdpack::insert_ref(key="lindley1965introduction",package="RelDists")

Author(s)

Freddy Hernandez fhernanb@unal.edu.co