DiscreteDists (version 1.0.0)

GGEO: The GGEO family

Description

The function GGEO() defines the Generalized Geometric distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

GGEO(mu.link = "logit", sigma.link = "log")

Value

Returns a gamlss.family object which can be used to fit a GGEO 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 "logit" link as the default for the sigma. Other links are "probit" and "cloglog"'(complementary log-log)

Author

Valentina Hurtado Sepúlveda,

Details

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

\(f(x | \mu, \sigma) = \frac{\sigma \mu^x (1-\mu)}{(1-(1-\sigma) \mu^{x+1})(1-(1-\sigma) \mu^{x})}\)

with \(0 < \mu < 1\) and \(\sigma > 0\). If \(\sigma=1\), the GGEO distribution reduces to the geometric distribution with success probability \(1-\mu\).

References

gomez2010DiscreteDists

See Also

dGGEO.

Examples

# Example 1
# Generating some random values with
# known mu and sigma
set.seed(123)
y <- rGGEO(n=200, mu=0.95, sigma=1.5)

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

# Extracting the fitted values for mu and sigma
# using the inverse link function
inv_logit <- function(x) 1/(1 + exp(-x))

inv_logit(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 ~ GGEO
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu    <- inv_logit(1.7 - 2.8*x1)
  sigma <- exp(0.73 + 1*x2)
  y <- rGGEO(n=n, mu=mu, sigma=sigma)
  data.frame(y=y, x1=x1, x2=x2)
}

set.seed(78353)
datos <- gendat(n=100)

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

summary(mod2)

# Example 3
# Number of accidents to 647 women working on H. E. Shells
# for 5 weeks. Taken from Gomez-Deniz (2010) page 411.

y <- rep(x=0:5, times=c(447, 132, 42, 21, 3, 2))

mod3 <- gamlss(y~1, family=GGEO,
               control=gamlss.control(n.cyc=500, trace=TRUE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
inv_logit <- function(x) 1/(1 + exp(-x))

inv_logit(coef(mod3, what="mu"))
exp(coef(mod3, what="sigma"))