dGammaW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Gamma Weibull distribution
with parameters mu
, sigma
, nu
and tau
.
dGammaW(x, mu, sigma, nu, log = FALSE) pGammaW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qGammaW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rGammaW(n, mu, sigma, nu) hGammaW(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 Gamma Weibull Distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= \frac{σ μ^{ν}}{Γ(ν)} x^{ν σ - 1} \exp(-μ x^σ),
for x > 0, μ > 0, σ ≥q 0 and ν > 0.
dGammaW
gives the density, pGammaW
gives the distribution
function, qGammaW
gives the quantile function, rGammaW
generates random deviates and hGammaW
gives the hazard function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
almalki2014modificationsRelDists
\insertRefstacy1962generalizationRelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dGammaW(x, mu = 0.5, sigma = 2, nu=1), from = 0, to = 6, col = "red", las = 1, ylab = "f(x)") ## The cumulative distribution and the Reliability function par(mfrow = c(1, 2)) curve(pGammaW(x, mu = 0.5, sigma = 2, nu=1), from = 0, to = 3, ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)") curve(pGammaW(x, mu = 0.5, sigma = 2, nu=1, lower.tail = FALSE), from = 0, to = 3, ylim = c(0, 1), col = "red", las = 1, ylab = "R(x)") ## The quantile function p <- seq(from = 0, to = 0.99999, length.out = 100) plot(x = qGammaW(p = p, mu = 0.5, sigma = 2, nu=1), y = p, xlab = "Quantile", las = 1, ylab = "Probability") curve(pGammaW(x, mu = 0.5, sigma = 2, nu=1), from = 0, add = TRUE, col = "red") ## The random function hist(rGammaW(1000, mu = 0.5, sigma = 2, nu=1), freq = FALSE, xlab = "x", ylim = c(0, 1), las = 1, main = "") curve(dGammaW(x, mu = 0.5, sigma = 2, nu=1), from = 0, add = TRUE, col = "red", ylim = c(0, 1)) ## The Hazard function par(mfrow=c(1,1)) curve(hGammaW(x, mu = 0.5, sigma = 2, nu=1), from = 0, to = 2, ylim = c(0, 1), col = "red", ylab = "Hazard function", las = 1) par(old_par) # restore previous graphical parameters
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