dEW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the exponentiated Weibull distribution with
parameters mu
, sigma
and nu
.
dEW(x, mu, sigma, nu, log = FALSE) pEW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qEW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rEW(n, mu, sigma, nu) hEW(x, mu, sigma, nu)
x, q |
vector of quantiles. |
mu |
scale parameter. |
sigma, nu |
shape parameters. |
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. |
The Exponentiated Weibull Distribution with parameters mu
,
sigma
and nu
has density given by
f(x)=ν μ σ x^{σ-1} \exp(-μ x^σ) (1-\exp(-μ x^σ))^{ν-1},
for x > 0, μ > 0, σ > 0 and ν > 0.
dEW
gives the density, pEW
gives the distribution
function, qEW
gives the quantile function, rEW
generates random deviates and hEW
gives the hazard function.
EW
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dEW(x, mu=2, sigma=1.5, nu=0.5), from=0, to=2, ylim=c(0, 2.5), col="red", las=1, ylab="f(x)") ## The cumulative distribution and the Reliability function par(mfrow=c(1, 2)) curve(pEW(x, mu=2, sigma=1.5, nu=0.5), from=0, to=2, col="red", las=1, ylab="F(x)") curve(pEW(x, mu=2, sigma=1.5, nu=0.5, lower.tail=FALSE), from=0, to=2, col="red", las=1, ylab="R(x)") ## The quantile function p <- seq(from=0, to=0.99999, length.out=100) plot(x=qEW(p, mu=2, sigma=1.5, nu=0.5), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pEW(x, mu=2, sigma=1.5, nu=0.5), from=0, add=TRUE, col="red") ## The random function hist(rEW(n=10000, mu=2, sigma=1.5, nu=0.5), freq=FALSE, xlab="x", las=1, main="") curve(dEW(x, mu=2, sigma=1.5, nu=0.5), from=0, add=TRUE, col="red") ## The Hazard function par(mfrow=c(1,1)) curve(hEW(x, mu=2, sigma=1.5, nu=0.5), from=0, to=2, ylim=c(0, 7), col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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