dExW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Extended Weibull distribution
with parameters mu
, sigma
and nu
.
dExW(x, mu, sigma, nu, log = FALSE) pExW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qExW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rExW(n, mu, sigma, nu) hExW(x, mu, sigma, nu)
x, q |
vector of quantiles. |
mu |
parameter. |
sigma |
parameter. |
nu |
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. |
The Extended Weibull distribution with parameters mu
,
sigma
and nu
has density given by
f(x) = \frac{μ σ ν x^{σ -1} exp({-μ x^{σ}})} {[1 -(1-ν) exp({-μ x^{σ}})]^2},
for x > 0.
dExW
gives the density, pExW
gives the distribution
function, qExW
gives the quantile function, rExW
generates random deviates and hExW
gives the hazard function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefZhang2007RelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dExW(x, mu=0.3, sigma=2, nu=0.05), 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(pExW(x, mu=0.3, sigma=2, nu=0.05), from=0.0001, to=2, col="red", las=1, ylab="F(x)") curve(pExW(x, mu=0.3, sigma=2, nu=0.05, 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=qExW(p, mu=0.3, sigma=2, nu=0.05), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pExW(x, mu=0.3, sigma=2, nu=0.05), from=0, add=TRUE, col="red") ## The random function hist(rExW(n=10000, mu=0.3, sigma=2, nu=0.05), freq=FALSE, xlab="x", ylim=c(0, 2), las=1, main="") curve(dExW(x, mu=0.3, sigma=2, nu=0.05), from=0.001, to=4, add=TRUE, col="red") ## The Hazard function curve(hExW(x, mu=0.3, sigma=2, nu=0.05), from=0.001, to=4, col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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