dMOEW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Marshall-Olkin Extended Weibull distribution
with parameters mu
, sigma
and nu
.
dMOEW(x, mu, sigma, nu, log = FALSE) pMOEW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qMOEW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rMOEW(n, mu, sigma, nu) hMOEW(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 Marshall-Olkin Extended Weibull distribution mu
,
sigma
and nu
has density given by
f(x) = \frac{μ σ ν (ν x)^{σ - 1} exp\{{-(ν x )^{σ}}\}}{\{1-(1-μ) exp\{{-(ν x )^{σ}}\} \}^{2}},
for x > 0.
dMOEW
gives the density, pMOEW
gives the distribution
function, qMOEW
gives the quantile function, rMOEW
generates random deviates and hMOEW
gives the hazard function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefghitany2005RelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0.001, to=1, col="red", ylab="f(x)", las=1) ## The cumulative distribution and the Reliability function par(mfrow=c(1, 2)) curve(pMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0.0001, to=2, col="red", las=1, ylab="F(x)") curve(pMOEW(x, mu=0.5, sigma=0.7, nu=1, 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=qMOEW(p, mu=0.5, sigma=0.7, nu=1), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0, add=TRUE, col="red") ## The random function hist(rMOEW(n=100, mu=0.5, sigma=0.7, nu=1), freq=FALSE, xlab="x", ylim=c(0, 1), las=1, main="") curve(dMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0.001, to=2, add=TRUE, col="red") ## The Hazard function curve(hMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0.001, to=3, col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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