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The Marshall-Olkin Extended Inverse Weibull distribution

Source: R/dMOEIW.R
dMOEIW.Rd

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.

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.

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.

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.

Author

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co

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