dMW function

The Modified Weibull distribution

Density, distribution function, quantile function, random generation and hazard function for the modified weibull distribution with parameters mu, sigma and nu.

dMW(x, mu, sigma, nu, log = FALSE)

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

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

rMW(n, mu, sigma, nu)

hMW(x, mu, sigma, nu)

Arguments

• x, q: vector of quantiles.
• mu: shape parameter one.
• sigma: parameter two.
• nu: scale parameter three.
• 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

dMW gives the density, pMW gives the distribution function, qMW gives the quantile function, rMW

generates random deviates and hMW gives the hazard function.

Details

The modified weibull distribution with parameters mu, sigma

and nu has density given by

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

for $x > 0$, $\mu > 0$, $\sigma \geq 0$ and $\nu \geq 0$.

Examples

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

## The probability density function 
curve(dMW(x, mu=2, sigma=1.5, nu=0.2), from=0, to=2,
  ylim=c(0, 1.5), col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pMW(x, mu=2, sigma=1.5, nu=0.2), from=0, to=2,
 col = "red", las=1, ylab="F(x)")
curve(pMW(x, mu=2, sigma=1.5, nu=0.2, lower.tail = FALSE), 
from=0, to=2, col="red", las=1, ylab ="R(x)")

## The quantile function
p <- seq(from=0, to=0.9999, length.out=100)
plot(x=qMW(p, mu=2, sigma=1.5, nu=0.2), y=p, xlab="Quantile",
 las=1, ylab="Probability")
curve(pMW(x, mu=2, sigma=1.5, nu=0.2), from=0, add=TRUE, col="red")

## The random function
hist(rMW(n=1000, mu=2, sigma=1.5, nu=0.2), freq=FALSE,
 xlab="x", las=1, main="")
curve(dMW(x, mu=2, sigma=1.5, nu=0.2), from=0, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hMW(x, mu=2, sigma=1.5, nu=0.2), from=0, to=1.5, ylim=c(0, 5),
 col="red", las=1, ylab="H(x)", las=1)

par(old_par) # restore previous graphical parameters

References

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

Rdpack::insert_ref(key="lai2003modified",package="RelDists")

Author(s)

Johan David Marin Benjumea, johand.marin@udea.edu.co