The hyper Poisson family (with mu as mean)

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

HYPERPO2(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.

Value

Returns a gamlss.family object which can be used to fit a hyper-Poisson distribution version 2 in the gamlss() function.

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

Sáez-Castillo, A. J., & Conde-Sánchez, A. (2013). A hyper-Poisson regression model for overdispersed and underdispersed count data. Computational Statistics & Data Analysis, 61, 148-157.

Author

Freddy Hernandez, fhernanb@unal.edu.co

Examples

# Example 1
# Generating some random values with
# known mu and sigma
set.seed(1234)
y <- rHYPERPO2(n=100, mu=4, sigma=1.5)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, sigma.fo=~1, family=HYPERPO2,
               control=gamlss.control(n.cyc=500, trace=TRUE))
#> GAMLSS-RS iteration 1: Global Deviance = 407.1684 
#> GAMLSS-RS iteration 2: Global Deviance = 407.1684 

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod1, what="mu"))
#> (Intercept) 
#>    3.579995 
exp(coef(mod1, what="sigma"))
#> (Intercept) 
#>    1.164629 

# Example 2
# Generating random values under some model

if (FALSE) { # \dontrun{
# 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(12345)
dat <- gendat(n=200)

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

summary(mod2)
} # }