RelDists (version 1.0.0)

EOFNH: The Extended Odd Frechet-Nadarjad-Hanhighi family

Description

The Extended Odd Frechet-Nadarjad-Hanhighi family

Usage

EOFNH(mu.link = "log", sigma.link = "log", nu.link = "log", tau.link = "log")

Value

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

tau.link

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

Author

Johan David Marin Benjumea,

Details

The Extended Odd Frechet-Nadarjad-Hanhighi distribution with parameters mu, sigma, nu and tau has density given by

\(f(x)= \frac{\mu\sigma\nu\tau(1+\nu x)^{\sigma-1}e^{(1-(1+\nu x)^\sigma)}[1-(1-e^{(1-(1+\nu x)^\sigma)})^{\mu}]^{\tau-1}}{(1-e^{(1-(1+\nu x)^{\sigma})})^{\mu\tau+1}} e^{-[(1-e^{(1-(1+\nu x)^\sigma)})^{-\mu}-1]^{\tau}},\)

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

References

nasiru2018extendedRelDists

See Also

dEOFNH

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rEOFNH(n=100, mu=1, sigma=2.1, nu=0.8, tau=1)

# Fitting the model
require(gamlss)

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

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

# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(0.5 + x1)
sigma <- exp(0.8 + x2)
nu <- 1
tau <- 0.5
x <- rEOFNH(n=n, mu, sigma, nu, tau)

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

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