dAddW function

The Additive Weibull distribution

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

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.

Returns

dAddW gives the density, pAddW gives the distribution function, qAddW gives the quantile function, rAddW

generates random deviates and hAddW gives the hazard function.

Details

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

$f(x) = (\mu\nu x^{\nu - 1} + \sigma\tau x^{\tau - 1}) \exp({-\mu x^{\nu} - \sigma x^{\tau} }),$

for x > 0.

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

References

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

Rdpack::insert_ref(key="Xie1996",package="RelDists")

Author(s)

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