dGIW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Generalized Inverse Weibull distribution
with parameters mu
, sigma
and nu
.
dGIW(x, mu, sigma, nu, log = FALSE) pGIW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qGIW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rGIW(n, mu, sigma, nu) hGIW(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 Generalized Inverse Weibull distribution mu
,
sigma
and nu
has density given by
f(x) = ν σ μ^{σ} x^{-(σ + 1)} exp \{-ν (\frac{μ}{x})^{σ}\},
for x > 0.
dGIW
gives the density, pGIW
gives the distribution
function, qGIW
gives the quantile function, rGIW
generates random deviates and hGIW
gives the hazard function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefgusmao2009RelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dGIW(x, mu=3, sigma=5, nu=0.5), from=0.001, to=8, col="red", ylab="f(x)", las=1) ## The cumulative distribution and the Reliability function par(mfrow=c(1, 2)) curve(pGIW(x, mu=3, sigma=5, nu=0.5), from=0.0001, to=14, col="red", las=1, ylab="F(x)") curve(pGIW(x, mu=3, sigma=5, nu=0.5, lower.tail=FALSE), from=0.0001, to=14, col="red", las=1, ylab="R(x)") ## The quantile function p <- seq(from=0, to=0.99999, length.out=100) plot(x=qGIW(p, mu=3, sigma=5, nu=0.5), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pGIW(x, mu=3, sigma=5, nu=0.5), from=0, add=TRUE, col="red") ## The random function hist(rGIW(n=1000, mu=3, sigma=5, nu=0.5), freq=FALSE, xlab="x", ylim=c(0, 0.8), las=1, main="") curve(dGIW(x, mu=3, sigma=5, nu=0.5), from=0.001, to=14, add=TRUE, col="red") ## The Hazard function curve(hGIW(x, mu=3, sigma=5, nu=0.5), from=0.001, to=30, col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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