POISXL function

The Discrete Poisson XLindley

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().

POISXL(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 Discrete Poisson XLindley distribution in the gamlss() function.

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.

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)

References

\insertRef ahsan2022DiscreteDists

See Also

dPOISXL .

Author(s)

Mariana Blandon Mejia, mblandonm@unal.edu.co