DMOLBE function

The DMOLBE family

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().

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.

Returns

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

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 $\sigma > 0$

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)

References

\insertRef Aljohani2023DiscreteDists

See Also

dDMOLBE .

Author(s)

Olga Usuga, olga.usuga@udea.edu.co