dRW {RelDists}

The Reflected Weibull distribution

Description

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.

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.

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.

Author(s)

Amylkar Urrea Montoya, [e-mail]

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.

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