DiscreteDists (version 1.1.1)

COMPO2: The COMPO2 family (with mu as mean)

Description

The function COMPO2() defines the Conway-Maxwell-Poisson distribution a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). This parameterization was proposed by Ribeiro et al. (2020) and the main characteristic is that \(E(X)=\mu\).

Usage

COMPO2(mu.link = "log", sigma.link = "identity")

Value

Returns a gamlss.family object which can be used to fit a COMPO2 distribution 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 "identity" link as the default for the sigma.

Author

Freddy Hernandez,

Details

The COMPO2 distribution with parameters \(\mu\) and \(\sigma\) has a support 0, 1, 2, ... and mass function given by

\(f(x | \mu, \sigma) = \left(\mu + \frac{\exp(\sigma)-1}{2 \exp(\sigma)} \right)^{x \exp(\sigma)} \frac{(x!)^{\exp(\sigma)}}{Z(\mu, \sigma)} \)

with \(\mu > 0\), \(\sigma \in \Re\) and

\(Z(\mu, \sigma)=\sum_{j=0}^{\infty} \frac{\mu^j}{(j!)^\sigma}\).

The proposed functions here are based on the functions from the COMPoissonReg package.

References

Ribeiro Jr, Eduardo E., et al. "Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data." Statistical Modelling 20.5 (2020): 443-466.

See Also

dCOMPO2.

Examples

# Example 1
# Generating some random values with
# known mu and sigma
y <- rCOMPO2(n=500, mu=10, sigma=-1)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, sigma.fo=~1, family=COMPO2,
               control=gamlss.control(n.cyc=500, trace=TRUE))

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

# Example 2
# Generating random values under some model

if (FALSE) {
# A function to simulate a data set with Y ~ COMPO2
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu    <- exp(2 + 1 * x1) # 12 approximately
  sigma <- 1 - 2 * x2      # 0 approximately
  y <- rCOMPO2(n=n, mu=mu, sigma=sigma)
  data.frame(y=y, x1=x1, x2=x2)
}

set.seed(123)
dat <- gendat(n=200)

# Fitting the model
mod2 <- NULL
mod2 <- gamlss(y~x1, sigma.fo=~x2, family=COMPO2, data=dat)

summary(mod2)
}