dLW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Log-Weibull distribution
with parameters mu
and sigma
.
dLW(x, mu, sigma, log = FALSE) pLW(q, mu, sigma, lower.tail = TRUE, log.p = FALSE) qLW(p, mu, sigma, lower.tail = TRUE, log.p = FALSE) rLW(n, mu, sigma) hLW(x, mu, sigma)
x, q |
vector of quantiles. |
mu |
parameter. |
sigma |
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 Log-Weibull Distribution with parameters mu
and sigma
has density given by
f(y)=(1/σ) e^{((y - μ)/σ)} exp\{-e^{((y - μ)/σ)}\},
for - infty
< y < infty
.
dLW
gives the density, pLW
gives the distribution
function, qLW
gives the quantile function, rLW
generates random deviates and hLW
gives the hazard function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefGumbel1958RelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dLW(x, mu=0, sigma=1.5), from=-8, to=5, col="red", las=1, ylab="f(x)") ## The cumulative distribution and the Reliability function par(mfrow=c(1, 2)) curve(pLW(x, mu=0, sigma=1.5), from=-8, to=5, col="red", las=1, ylab="F(x)") curve(pLW(x, mu=0, sigma=1.5, lower.tail=FALSE), from=-8, to=5, col="red", las=1, ylab="R(x)") ## The quantile function p <- seq(from=0, to=0.99999, length.out=100) plot(x=qLW(p, mu=0, sigma=1.5), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pLW(x, mu=0, sigma=1.5), from=-8, to=5, add=TRUE, col="red") ## The random function hist(rLW(n=10000, mu=0, sigma=1.5), freq=FALSE, xlab="x", las=1, main="") curve(dLW(x, mu=0, sigma=1.5), from=-15, to=6, add=TRUE, col="red") ## The Hazard function par(mfrow=c(1,1)) curve(hLW(x, mu=0, sigma=1.5), from=-8, to=7, col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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