PL {RelDists}

The Power Lindley family

Description

Power Lindley distribution

Usage

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.

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.

Value

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

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010.

Ghitanya ME, Al-Mutairi DK, Balakrishnanb N, Al-Enezi LJ (2013). “Power Lindley distribution and associated inference.” Computational Statistics and Data Analysis, 64, 20–33. doi:10.1016/j.csda.2013.02.026.

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")