dEGG function

The four parameter Exponentiated Generalized Gamma distribution

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.

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.

Returns

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.

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

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="cordeiro2011",package="RelDists")

Author(s)

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co