dWG | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the weibull geometric distribution with
parameters mu
, sigma
and nu
.
dWG(x, mu, sigma, nu, log = FALSE) pWG(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qWG(p, sigma, mu, nu, lower.tail = TRUE, log.p = FALSE) rWG(n, mu, sigma, nu) hWG(x, mu, sigma, nu)
x, q |
vector of quantiles. |
mu |
scale parameter. |
sigma |
shape parameter. |
nu |
parameter of geometric random variable. |
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 Weibull geometric distribution with parameters mu
,
sigma
and nu
has density given by
f(x) = (σ μ^σ (1-ν) x^(σ - 1) \exp(-(μ x)^σ)) (1- ν \exp(-(μ x)^σ))^{-2},
for x > 0, μ > 0, σ > 0 and 0 < ν < 1.
dWG
gives the density, pWG
gives the distribution
function, qWG
gives the quantile function, rWG
generates random deviates and hWG
gives the hazard function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
barreto2011weibullRelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, to = 3, ylim = c(0, 1.1), col = "red", las = 1, ylab = "f(x)") ## The cumulative distribution and the Reliability function par(mfrow = c(1, 2)) curve(pWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, to = 3, ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)") curve(pWG(x, mu = 0.9, sigma = 2, nu = 0.5, 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 = qWG(p = p, mu = 0.9, sigma = 2, nu = 0.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability") curve(pWG(x,mu = 0.9, sigma = 2, nu = 0.5), from = 0, add = TRUE, col = "red") ## The random function hist(rWG(1000, mu = 0.9, sigma = 2, nu = 0.5), freq = FALSE, xlab = "x", ylim = c(0, 1.8), las = 1, main = "") curve(dWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, add = TRUE, col = "red", ylim = c(0, 1.8)) ## The Hazard function( par(mfrow=c(1,1)) curve(hWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, to = 8, ylim = c(0, 12), col = "red", ylab = "Hazard function", las = 1) par(old_par) # restore previous graphical parameters
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