RelDists (version 1.0.0)

PL: The Power Lindley family

Description

Power Lindley distribution

Usage

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

Value

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

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.

Author

Amylkar Urrea Montoya,

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.

References

almalki2014modificationsRelDists

Ghitanya2013RelDists

See Also

dPL

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")