Density, distribution function, quantile function,
random generation and hazard function for the four parameter Exponentiated Generalized Gamma distribution
with parameters mu, sigma, nu and tau.
Usage
dEGG(x, mu, sigma, nu, tau, log = FALSE)
pEGG(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)
qEGG(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)
rEGG(n, mu, sigma, nu, tau)
hEGG(x, mu, sigma, nu, tau)Arguments
- x, q
vector of quantiles.
- mu
parameter.
- sigma
parameter.
- nu
parameter.
- tau
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.
Value
dEGG gives the density, pEGG gives the distribution
function, qEGG gives the quantile function, rEGG
generates random deviates and hEGG gives the hazard function.
Details
Four-Parameter Exponentiated Generalized Gamma distribution with parameters mu,
sigma, nu and tau has density given by
\(f(x) = \frac{\nu \sigma}{\mu \Gamma(\tau)} \left(\frac{x}{\mu}\right)^{\sigma \tau -1} \exp\left\{ - \left( \frac{x}{\mu} \right)^\sigma \right\} \left\{ \gamma_1\left( \tau, \left( \frac{x}{\mu} \right)^\sigma \right) \right\}^{\nu-1} ,\)
for x > 0.
References
Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32--55. doi:10.1016/j.ress.2013.11.010 .
Gauss M. C, Edwin M.M O, Giovana O. S (2011). “The exponentiated generalized gamma distribution with application to lifetime data.” Journal of Statistical Computation and Simulation, 81(7), 827--842. doi:10.1080/00949650903517874 .
Author
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
Examples
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters
## The probability density function
curve(dEGG(x, mu=0.1, sigma=0.8, nu=10, tau=1.5), from=0.000001, to=1.5, ylim=c(0, 2.5),
col="red", las=1, ylab="f(x)")
## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pEGG(x, mu=0.1, sigma=0.8, nu=10, tau=1.5),
from=0.000001, to=1.5, col="red", las=1, ylab="F(x)")
curve(pEGG(x, mu=0.1, sigma=0.8, nu=10, tau=1.5, lower.tail=FALSE),
from=0.000001, to=1.5, col="red", las=1, ylab="R(x)")
## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qEGG(p, mu=0.1, sigma=0.8, nu=10, tau=1.5), y=p, xlab="Quantile",
las=1, ylab="Probability")
curve(pEGG(x, mu=0.1, sigma=0.8, nu=10, tau=1.5),
from=0.00001, add=TRUE, col="red")
## The random function
hist(rEGG(n=100, mu=0.1, sigma=0.8, nu=10, tau=1.5), freq=FALSE,
xlab="x", las=1, main="")
curve(dEGG(x, mu=0.1, sigma=0.8, nu=10, tau=1.5),
from=0.0001, to=2, add=TRUE, col="red")
## The Hazard function
curve(hEGG(x, mu=0.1, sigma=0.8, nu=10, tau=1.5), from=0.0001, to=1.5,
col="red", ylab="Hazard function", las=1)
par(old_par) # restore previous graphical parameters
