dMOEIW {RelDists}

The Marshall-Olkin Extended Inverse Weibull distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Marshall-Olkin Extended Inverse Weibull distribution with parameters mu, sigma and nu.

Usage

dMOEIW(x, mu, sigma, nu, log = FALSE)

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

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

rMOEIW(n, mu, sigma, nu)

hMOEIW(x, mu, sigma, nu)

Arguments

x, q

vector of quantiles.

mu

parameter.

sigma

parameter.

nu

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

The Marshall-Olkin Extended Inverse Weibull distribution mu, sigma and nu has density given by

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

for x > 0.

Value

dMOEIW gives the density, pMOEIW gives the distribution function, qMOEIW gives the quantile function, rMOEIW generates random deviates and hMOEIW gives the hazard function.

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Hassan M O, A.H E, A.M.K T, Abdulkareem M Bc (2017). “Extended inverse Weibull distribution with reliability application.” Journal of the Egyptian Mathematical Society, 25, 343–349. doi:10.1016/j.joems.2017.02.006, http://dx.doi.org/10.1016/j.joems.2017.02.006.

Examples

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

## The probability density function
curve(dMOEIW(x, mu=0.6, sigma=1.7, nu=0.3), from=0, to=2,
      col="red", ylab="f(x)", las=1)

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pMOEIW(x, mu=0.6, sigma=1.7, nu=0.3),
      from=0.0001, to=2, col="red", las=1, ylab="F(x)")
curve(pMOEIW(x, mu=0.6, sigma=1.7, nu=0.3, lower.tail=FALSE),
      from=0.0001, to=2, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qMOEIW(p, mu=0.6, sigma=1.7, nu=0.3), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pMOEIW(x, mu=0.6, sigma=1.7, nu=0.3),
      from=0, add=TRUE, col="red")

## The random function
hist(rMOEIW(n=1000, mu=0.6, sigma=1.7, nu=0.3), freq=FALSE,
     xlab="x", las=1, main="")
curve(dMOEIW(x, mu=0.6, sigma=1.7, nu=0.3),
      from=0.001, to=4, add=TRUE, col="red")

## The Hazard function
curve(hMOEIW(x, mu=0.5, sigma=0.7, nu=1), from=0.001, to=3,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters