QXGP function

The Quasi XGamma Poisson family

QXGP(mu.link = "log", sigma.link = "log", nu.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.
• nu.link: defines the nu.link, with "log" link as the default for the nu parameter.

Returns

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

Details

The Quasi XGamma Poisson distribution with parameters mu, sigma and nu has density given by

c("$f(x)= K(\\mu, \\sigma, \\nu)(\\frac {\\sigma^{2} x^{2}}{2} + \\mu)\n$", "$exp(\\frac{\\nu exp(-\\sigma x)(1 + \\mu + \\sigma x + \\frac {\\sigma^{2}x^{2}}{2})}{1+\\mu} - \\sigma x),$")

for $x > 0$, $\mu> 0$, $\sigma> 0$, $\nu> 1$.

where

$K(\mu, \sigma, \nu) = \frac{\nu \sigma}{(exp(\nu)-1)(1+\mu)}$

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rQXGP(n=200, mu=4, sigma=2, nu=3)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='QXGP',
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu, sigma and nu
# using the inverse link function
exp(coef(mod, what='mu'))
exp(coef(mod, what='sigma'))
exp(coef(mod, what='nu'))

# Example 2
# Generating random values under some model
n <- 2000
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(-2.19 + 3 * x1)
sigma <- exp(1 - 2 * x2)
nu <- 1
x <- rQXGP(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=QXGP,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")
exp(coef(mod, what="nu"))

References

Rdpack::insert_ref(key="subhradev2018",package="RelDists")

See Also

dQXGP

Author(s)

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co