The Reflected Weibull distribution

Density, distribution function, quantile function, random generation and hazard function for the Reflected Weibull Distribution with parameters mu and sigma.

Usage

dRW(x, mu, sigma, log = FALSE)

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

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

rRW(n, mu, sigma)

hRW(x, mu, sigma)

Arguments

x, q: vector of quantiles.
mu: parameter.
sigma: 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

dRW gives the density, pRW gives the distribution function, qRW gives the quantile function, rRW generates random deviates and hRW gives the hazard function.

Details

The Reflected Weibull Distribution with parameters mu and sigma has density given by

\(f(y) = \mu\sigma (-y) ^{\sigma - 1} e ^ {-\mu(-y)^\sigma},\)

for y < 0.

References

Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010 .

Clifford Cohen A (1973). “The Reflected Weibull Distribution.” Technometrics, 15(4), 867–873. doi:10.2307/1267396 .

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(dRW(x, mu=1, sigma=1), from=-5, to=-0.01,
      col="red", las=1, ylab="f(x)")


## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pRW(x, mu=1, sigma=1),
      from=-5, to=-0.01, col="red", las=1, ylab="F(x)")
curve(pRW(x, mu=1, sigma=1, lower.tail=FALSE),
      from=-5, to=-0.01, col="red", las=1, ylab="R(x)")


## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qRW(p, mu=1, sigma=1), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pRW(x, mu=1, sigma=1), from=-5, add=TRUE, col="red")

## The random function
hist(rRW(n=10000, mu=1, sigma=1), freq=FALSE,
     xlab="x", las=1, main="")
curve(dRW(x, mu=1, sigma=1), from=-5, to=-0.01, add=TRUE, col="red")


## The Hazard function
par(mfrow=c(1,1))
curve(hRW(x, mu=1, sigma=1), from=-0.3, to=-0.01,
      col="red", ylab="Hazard function", las=1)


par(old_par) # restore previous graphical parameters