POISXL {DiscreteDists} | R Documentation |
The Discrete Poisson XLindley
Description
The function POISXL()
defines the Discrete Poisson XLindley distribution, one-parameter
discrete distribution, for a gamlss.family
object to be used in GAMLSS fitting
using the function gamlss()
.
Usage
POISXL(mu.link = "log")
Arguments
mu.link |
defines the mu.link, with "log" link as the default for the mu parameter. |
Details
The Discrete Poisson XLindley distribution with parameters \mu
has a support
0, 1, 2, ... and mass function given by
f(x | \mu) = \frac{\mu^2(x+\mu^2+3(1+\mu))}{(1+\mu)^{4+x}}
; with \mu>0
.
Note: in this implementation we changed the original parameters \alpha
for \mu
,
we did it to implement this distribution within gamlss framework.
Value
Returns a gamlss.family
object which can be used
to fit a Discrete Poisson XLindley distribution
in the gamlss()
function.
Author(s)
Mariana Blandon Mejia, mblandonm@unal.edu.co
References
Ahsan-ul-Haq M, Al-Bossly A, El-Morshedy M, Eliwa MS, others (2022). “Poisson XLindley distribution for count data: statistical and reliability properties with estimation techniques and inference.” Computational Intelligence and Neuroscience, 2022.
See Also
Examples
# Example 1
# Generating some random values with
# known mu
y <- rPOISXL(n=1000, mu=1)
# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, family=POISXL,
control=gamlss.control(n.cyc=500, trace=FALSE))
# Extracting the fitted values for mu
# using the inverse link function
exp(coef(mod1, what='mu'))
# Example 2
# Generating random values under some model
# A function to simulate a data set with Y ~ POISXL
gendat <- function(n) {
x1 <- runif(n, min=0.4, max=0.6)
mu <- exp(1.21 - 3 * x1) # 0.75 approximately
y <- rPOISXL(n=n, mu=mu)
data.frame(y=y, x1=x1)
}
dat <- gendat(n=1500)
# Fitting the model
mod2 <- NULL
mod2 <- gamlss(y~x1, family=POISXL, data=dat,
control=gamlss.control(n.cyc=500, trace=FALSE))
summary(mod2)