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