dEOFNH: The Extended Odd Frechet-Nadarajah-Haghighi

In ousuga/RelDists: Estimation for some Reliability Distributions

The Extended Odd Frechet-Nadarajah-Haghighi

Description

Density, distribution function, quantile function, random generation and hazard function for the Extended Odd Fr?chet-Nadarajah-Haghighi distribution with parameters mu, sigma, nu and tau.

Usage

dEOFNH(x, mu, sigma, nu, tau, log = FALSE)

pEOFNH(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)

qEOFNH(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)

rEOFNH(n, mu, sigma, nu, tau)

hEOFNH(x, mu, sigma, nu, tau)

Arguments

x, q	vector of quantiles.
mu	parameter.
sigma	parameter.
nu	parameter.
tau	parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

Tthe Extended Odd Frechet-Nadarajah-Haghighi 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

dEOFNH gives the density, pEOFNH gives the distribution function, qEOFNH gives the quantile function, rEOFNH generates random numbers and hEOFNH gives the hazard 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.

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

##The probability density function
par(mfrow=c(1, 1))

curve(dEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), 
      from=0, to=10, ylim=c(0, 0.25), 
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pEOFNH(x,mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from = 0, to = 10, 
ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)")
curve(pEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1, lower.tail = FALSE), 
from = 0, to = 10, ylim = c(0, 1), col = "red", las = 1, ylab = "R(x)")

##The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qEOFNH(p, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, add=TRUE, col="red")

##The random function
hist(rEOFNH(n=10000, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), freq=FALSE,
     xlab="x", las=1, main="")
curve(dEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, add=TRUE, col="red", ylim=c(0,1.25))

##The Hazard function
par(mfrow=c(1,1))
curve(hEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, to=10, ylim=c(0, 1),
     col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters

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