dRW function

The Reflected Weibull distribution

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

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.

Returns

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.

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

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="Clifford1973",package="RelDists")

Author(s)

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