PL function

The Power Lindley family

Power Lindley distribution

PL(mu.link = "log", sigma.link = "log")

Arguments

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

Returns

Returns a gamlss.family object which can be used to fit a PL distribution in the gamlss() function.

Details

The Power Lindley Distribution with parameters mu

and sigma has density given by

$f(x) = \frac{\mu \sigma^2}{\sigma + 1} (1 + x^\mu) x ^ {\mu - 1} \exp({-\sigma x ^\mu}),$

for x > 0.

Examples

# Example 1
# Generating some random values with
# known mu and sigma 
y <- rPL(n=100, mu=1.5, sigma=0.2)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, family= 'PL',
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod, 'mu'))
exp(coef(mod, 'sigma'))

# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(1.2 - 2 * x1)
sigma <- exp(0.8 - 3 * x2)
x <- rPL(n=n, mu, sigma)

mod <- gamlss(x~x1, sigma.fo=~x2, family=PL,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="Ghitanya2013",package="RelDists")

See Also

dPL

Author(s)

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co