dGGD | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the generalized Gompertz distribution with
parameters mu
sigma
and nu
.
dGGD(x, mu, sigma, nu, log = FALSE) pGGD(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qGGD(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rGGD(n, mu, sigma, nu) hGGD(x, mu, sigma, nu)
x, q |
vector of quantiles. |
mu, nu |
scale parameter. |
sigma |
shape parameters. |
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 Gompertz Distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= ν μ \exp(-\frac{μ}{σ}(\exp(σ x - 1))) (1 - \exp(-\frac{μ}{σ}(\exp(σ x - 1))))^{(ν - 1)} ,
for x ≥q 0, μ > 0, σ ≥q 0 and ν > 0.
dGGD
gives the density, pGGD
gives the distribution
function, qGGD
gives the quantile function, rGGD
generates random deviates and hGGD
gives the hazard function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
el2013generalizedRelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function par(mfrow = c(1, 1)) curve(dGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, to = 4, col = "red", las = 1, ylab = "f(x)") ## The cumulative distribution and the Reliability function par(mfrow = c(1, 2)) curve(pGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, to = 4, ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)") curve(pGGD(x, mu=1, sigma=0.3, nu=1.5, lower.tail = FALSE), from = 0, to = 4, 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 = qGGD(p=p, mu=1, sigma=0.3, nu=1.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability") curve(pGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, add = TRUE, col = "red") ## The random function hist(rGGD(1000, mu=1, sigma=0.3, nu=1.5), freq = FALSE, xlab = "x", las = 1, ylim = c(0, 0.7), main = "") curve(dGGD(x,mu=1, sigma=0.3, nu=1.5), from = 0, to =8, add = TRUE, col = "red") ## The Hazard function par(mfrow=c(1,1)) curve(hGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, to = 3, col = "red", ylab = "The hazard function", las = 1) par(old_par) # restore previous graphical parameters
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