DMOLBE: The DMOLBE family

In DiscreteDists: Discrete Statistical Distributions

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, [e-mail]

References

\insertRef

Aljohani2023DiscreteDists

See Also

dDMOLBE.

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)

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