HYPERPO2 function

The hyper Poisson family (with mu as mean)

The hyper Poisson family (with mu as mean)

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().

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.

Returns

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 μ\mu and σ\sigma

has a support 0, 1, 2, ...

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

to λ\lambda parameter.

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 # 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)

References

\insertRef saez2013hyperpoDiscreteDists

See Also

dHYPERPO2 , HYPERPO .

Author(s)

Freddy Hernandez, fhernanb@unal.edu.co

  • Maintainer: Freddy Hernandez-Barajas
  • License: MIT + file LICENSE
  • Last published: 2024-09-13