dEOFNH {RelDists}

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

References

Nasiru S (2018). “Extended Odd Fréchet-G Family of Distributions.” Journal of Probability and Statistics, 2018.

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