DiscreteDists (version 1.0.0)

HYPERPO2: The hyper Poisson family (with mu as mean)

Description

The function HYPERPO2() defines the hyper Poisson distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

HYPERPO2(mu.link = "log", sigma.link = "log")

Value

Returns a gamlss.family object which can be used to fit a hyper-Poisson distribution version 2 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

Freddy Hernandez,

Details

The hyper-Poisson distribution with parameters \(\mu\) and \(\sigma\) has a support 0, 1, 2, ...

Note: in this implementation the parameter \(\mu\) is the mean of the distribution and \(\sigma\) corresponds to the dispersion parameter. If you fit a model with this parameterization, the time will increase because an internal procedure to convert \(\mu\) to \(\lambda\) parameter.

References

saez2013hyperpoDiscreteDists

See Also

dHYPERPO2, HYPERPO.

Examples

# Example 1
# Generating some random values with
# known mu and sigma
set.seed(1234)
y <- rHYPERPO2(n=200, mu=3, sigma=0.5)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, sigma.fo=~1, family=HYPERPO2,
               control=gamlss.control(n.cyc=500, trace=FALSE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod1, what='mu'))
exp(coef(mod1, what='sigma'))

# Example 2
# Generating random values under some model

# \donttest{
# A function to simulate a data set with Y ~ HYPERPO2
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu    <- exp(1.21 - 3 * x1) # 0.75 approximately
  sigma <- exp(1.26 - 2 * x2) # 1.30 approximately
  y <- rHYPERPO2(n=n, mu=mu, sigma=sigma)
  data.frame(y=y, x1=x1, x2=x2)
}

set.seed(1234)
datos <- gendat(n=500)

mod2 <- NULL
mod2 <- gamlss(y~x1, sigma.fo=~x2, family=HYPERPO2, data=datos,
               control=gamlss.control(n.cyc=500, trace=FALSE))

summary(mod2)
# }