dRW: The Reflected Weibull distribution

In ousuga/RelDists: Estimation for some Reliability Distributions

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) = μσ (-y) ^{σ - 1} e ^ {-μ(-y)^σ},

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

\insertRef

almalki2014modificationsRelDists

\insertRef

Clifford1973RelDists

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

ousuga/RelDists documentation built on Jan. 12, 2023, 10:27 p.m.