dGMW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the generalized
modified weibull distribution with parameters mu
,
sigma
, nu
and tau
.
dGMW(x, mu, sigma, nu, tau, log = FALSE) pGMW(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE) qGMW(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE) rGMW(n, mu, sigma, nu, tau) hGMW(x, mu, sigma, nu, tau, log = FALSE)
x, q |
vector of quantiles. |
mu |
scale parameter. |
sigma |
shape parameter. |
nu |
shape parameter. |
tau |
acceleration 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 modified weibull with parameters mu
,
sigma
, nu
and tau
has density given by
f(x)= μ σ x^{ν - 1}(ν + τ x) \exp(τ x - μ x^{ν} e^{τ x}) [1 - \exp(- μ x^{ν} e^{τ x})]^{σ-1},
for x>0.
dGMW
gives the density, pGMW
gives the distribution
function, qGMW
gives the quantile function, rGMW
generates random deviates and hGMW
gives the hazard function.
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, to=0.8, ylim=c(0, 2), col="red", las=1, ylab="f(x)") ## The cumulative distribution and the Reliability function par(mfrow=c(1, 2)) curve(pGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, to=1.2, col="red", las=1, ylab="F(x)") curve(pGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5, lower.tail=FALSE), from=0, to=1.2, col="red", las=1, ylab="R(x)") ## The quantile function p <- seq(from=0, to=0.99999, length.out=100) plot(x=qGMW(p, mu=2, sigma=0.5, nu=2, tau=1.5), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, add=TRUE, col="red") ## The random function hist(rGMW(n=1000, mu=2, sigma=0.5, nu=2,tau=1.5), freq=FALSE, xlab="x", main ="", las=1) curve(dGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, add=TRUE, col="red") ## The Hazard function par(mfrow=c(1,1)) curve(hGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, to=1, ylim=c(0, 16), col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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