DBH: The Discrete Burr Hatke family
| DBH | R Documentation |
The Discrete Burr Hatke family
Description
The function DBH() defines the Discrete Burr Hatke distribution, one-parameter
discrete distribution, for a gamlss.family object to be used in GAMLSS fitting
using the function gamlss().
Usage
DBH(mu.link = "logit")
Arguments
mu.link |
defines the mu.link, with "logit" link as the default for the mu parameter. Other links are "probit" and "cloglog"'(complementary log-log) |
Details
The Discrete Burr-Hatke distribution with parameters \mu has a support
0, 1, 2, ... and density given by
f(x | \mu) = (\frac{1}{x+1}-\frac{\mu}{x+2})\mu^{x}
The pmf is log-convex for all values of 0 < \mu < 1, where \frac{f(x+1;\mu)}{f(x;\mu)}
is an increasing function in x for all values of the parameter \mu.
Note: in this implementation we changed the original parameters \lambda for \mu,
we did it to implement this distribution within gamlss framework.
Value
Returns a gamlss.family object which can be used
to fit a Discrete Burr-Hatke distribution
in the gamlss() function.
Author(s)
Valentina Hurtado Sepulveda, vhurtados@unal.edu.co
References
\insertRefel2020discreteDiscreteDists
See Also
dDBH.
Examples
# Example 1
# Generating some random values with
# known mu
y <- rDBH(n=1000, mu=0.74)
library(gamlss)
mod1 <- gamlss(y~1, family=DBH,
control=gamlss.control(n.cyc=500, trace=FALSE))
# Extracting the fitted values for mu
# using the inverse logit function
inv_logit <- function(x) exp(x) / (1+exp(x))
inv_logit(coef(mod1, parameter="mu"))
# Example 2
# Generating random values under some model
# A function to simulate a data set with Y ~ DBH
gendat <- function(n) {
x1 <- runif(n)
mu <- inv_logit(-3 + 5 * x1)
y <- rDBH(n=n, mu=mu)
data.frame(y=y, x1=x1)
}
datos <- gendat(n=150)
mod2 <- NULL
mod2 <- gamlss(y~x1, family=DBH, data=datos,
control=gamlss.control(n.cyc=500, trace=FALSE))
summary(mod2)
# Example 3
# number of carious teeth among the four deciduous molars.
# Taken from EL-MORSHEDY (2020) page 74364.
y <- rep(0:4, times=c(64, 17, 10, 6, 3))
mod3 <- gamlss(y~1, family=DBH,
control=gamlss.control(n.cyc=500, trace=FALSE))
# Extracting the fitted values for mu
# using the inverse link function
inv_logit <- function(x) 1/(1 + exp(-x))
inv_logit(coef(mod3, what="mu"))
