EOFNH: The Extended Odd Frechet-Nadarajah-Haghighi family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Extended Odd Frechet-Nadarajah-Haghighi family

Description

The Extended Odd Frechet-Nadarjad-Hanhighi family

Usage

EOFNH(mu.link = "log", sigma.link = "log", nu.link = "log", tau.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.
tau.link	defines the tau.link, with "log" link as the default for the tau parameter.

Details

The Extended Odd Frechet-Nadarajah-Haghighi 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.

Value

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

Author(s)

Helber Santiago Padilla, [e-mail]

References

Nasiru, S. (2018). Extended Odd Fréchet‐G Family of Distributions Journal of Probability and Statistics, 2018(1), 2931326.

\insertRef

nasiru2018extendedRelDists

See Also

dEOFNH

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
set.seed(123)
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 the model
n <- 100
x1 <- runif(n)
x2 <- runif(n)
mu <- exp(0.5 - 1.2 * x1)
sigma <- 2.1
nu <- 0.8
tau <- 1
y <- rEOFNH(n=n, mu, sigma, nu, tau)

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

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

ousuga/RelDists documentation built on March 29, 2025, 4:07 a.m.