DMOLBE {DiscreteDists} | R Documentation |
The DMOLBE family
Description
The function DMOLBE()
defines the Discrete Marshall-Olkin Length Biased
Exponential distribution, a two parameter
distribution, for a gamlss.family
object to be used in GAMLSS fitting
using the function gamlss()
.
Usage
DMOLBE(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. |
Details
The DMOLBE distribution with parameters \mu
and \sigma
has a support 0, 1, 2, ... and mass function given by
f(x | \mu, \sigma) = \frac{\sigma ((1+x/\mu)\exp(-x/\mu)-(1+(x+1)/\mu)\exp(-(x+1)/\mu))}{(1-(1-\sigma)(1+x/\mu)\exp(-x/\mu)) ((1-(1-\sigma)(1+(x+1)/\mu)\exp(-(x+1)/\mu))}
with \mu > 0
and \sigma > 0
Value
Returns a gamlss.family
object which can be used
to fit a DMOLBE distribution
in the gamlss()
function.
Author(s)
Olga Usuga, olga.usuga@udea.edu.co
References
Aljohani HM, Ahsan-ul-Haq M, Zafar J, Almetwally EM, Alghamdi AS, Hussam E, Muse AH (2023). “Analysis of Covid-19 data using discrete Marshall-Olkinin Length Biased Exponential: Bayesian and frequentist approach.” Scientific Reports, 13(1), 12243.
See Also
Examples
# Example 1
# Generating some random values with
# known mu and sigma
set.seed(1234)
y <- rDMOLBE(n=100, mu=10, sigma=7)
# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, sigma.fo=~1, family=DMOLBE,
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 ~ DMOLBE
gendat <- function(n) {
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(1.21 - 3 * x1) # 0.75 approximately
sigma <- exp(1.26 - 2 * x2) # 1.30 approximately
y <- rDMOLBE(n=n, mu=mu, sigma=sigma)
data.frame(y=y, x1=x1,x2=x2)
}
set.seed(123)
dat <- gendat(n=350)
# Fitting the model
mod2 <- NULL
mod2 <- gamlss(y~x1, sigma.fo=~x2, family=DMOLBE, data=dat,
control=gamlss.control(n.cyc=500, trace=FALSE))
summary(mod2)