DIKUM: The discrete Inverted Kumaraswamy family

In DiscreteDists: Discrete Statistical Distributions

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")

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 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.

Value

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

Author(s)

Daniel Felipe Villa Rengifo, [e-mail]

References

\insertRef

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)

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