GGEO: The GGEO family

In DiscreteDists: Discrete Statistical Distributions

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")

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)

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.

Value

Returns a gamlss.family object which can be used to fit a GGEO distribution in the gamlss() function.

Author(s)

Valentina Hurtado Sepúlveda, [e-mail]

References

\insertRef

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"))

DiscreteDists documentation built on Sept. 14, 2024, 1:07 a.m.