dAddW: The Additive Weibull distribution

In ousuga/RelDists: Estimation for some Reliability Distributions

The Additive Weibull distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Additive Weibull distribution with parameters mu, sigma, nu and tau.

Usage

dAddW(x, mu, sigma, nu, tau, log = FALSE)

pAddW(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)

qAddW(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)

rAddW(n, mu, sigma, nu, tau)

hAddW(x, mu, sigma, nu, tau)

Arguments

x, q	vector of quantiles.
mu	parameter.
sigma	parameter.
nu	shape parameter.
tau	shape 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

Additive Weibull Distribution with parameters mu, sigma, nu and tau has density given by

f(x) = (μν x^{ν - 1} + στ x^{τ - 1}) \exp({-μ x^{ν} - σ x^{τ} }),

for x > 0.

Value

dAddW gives the density, pAddW gives the distribution function, qAddW gives the quantile function, rAddW generates random deviates and hAddW gives the hazard function.

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

Xie1996RelDists

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
curve(dAddW(x, mu=1.5, sigma=0.5, nu=3, tau=0.8), from=0.0001, to=2,
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pAddW(x, mu=1.5, sigma=0.5, nu=3, tau=0.8),
      from=0.0001, to=2, col="red", las=1, ylab="F(x)")
curve(pAddW(x, mu=1.5, sigma=0.5, nu=3, tau=0.8, lower.tail=FALSE),
      from=0.0001, to=2, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qAddW(p, mu=1.5, sigma=0.2, nu=3, tau=0.8), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pAddW(x, mu=1.5, sigma=0.2, nu=3, tau=0.8), 
      from=0, add=TRUE, col="red")

## The random function
hist(rAddW(n=10000, mu=1.5, sigma=0.2, nu=3, tau=0.8), freq=FALSE,
     xlab="x", las=1, main="")
curve(dAddW(x, mu=1.5, sigma=0.2, nu=3, tau=0.8),
      from=0.09, to=5, add=TRUE, col="red")

## The Hazard function
curve(hAddW(x, mu=1.5, sigma=0.2, nu=3, tau=0.8), from=0.001, to=1,
      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.