DiscreteDists (version 1.0.0)

DIKUM: The discrete Inverted Kumaraswamy family

Description

The function DIKUM() defines the discrete Inverted Kumaraswamy distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

DIKUM(mu.link = "log", sigma.link = "log")

Value

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

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.

Author

Daniel Felipe Villa Rengifo,

Details

The discrete Inverted Kumaraswamy distribution with parameters \(\mu\) and \(\sigma\) has a support 0, 1, 2, ... and density given by

\(f(x | \mu, \sigma) = (1-(2+x)^{-\mu})^{\sigma}-(1-(1+x)^{-\mu})^{\sigma}\)

with \(\mu > 0\) and \(\sigma > 0\).

Note: in this implementation we changed the original parameters \(\alpha\) and \(\beta\) for \(\mu\) and \(\sigma\) respectively, we did it to implement this distribution within gamlss framework.

References

EL_Helbawy2022DiscreteDists

See Also

dDIKUM.

Examples

# Example 1
# Generating some random values with
# known mu and sigma
set.seed(150)
y <- rDIKUM(1000, mu=1, sigma=5)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y ~ 1, sigma.fo = ~1, family=DIKUM,
               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

library(gamlss)

# A function to simulate a data set with Y ~ DIKUM
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 <- rDIKUM(n=n, mu=mu, sigma=sigma)
  data.frame(y=y, x1=x1, x2=x2)
}

dat <- gendat(n=150)

# Fitting the model
mod2 <- gamlss(y ~ x1, sigma.fo = ~x2, family = "DIKUM", data=dat,
               control=gamlss.control(n.cyc=500, trace=FALSE))

summary(mod2)