RelDists (version 1.0.0)

QXGP: The Quasi XGamma Poisson family

Description

The Quasi XGamma Poisson family

Usage

QXGP(mu.link = "log", sigma.link = "log", nu.link = "log")

Value

Returns a gamlss.family object which can be used to fit a QXGP 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.

nu.link

defines the nu.link, with "log" link as the default for the nu parameter.

Author

Amylkar Urrea Montoya,

Details

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

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

for \(x > 0\), \(\mu> 0\), \(\sigma> 0\), \(\nu> 1\).

where

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

References

subhradev2018RelDists

See Also

dQXGP

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"))