RelDists (version 1.0.0)

dAddW: 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)

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.

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.

Author

Amylkar Urrea Montoya,

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.

References

almalki2014modificationsRelDists

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