dEGG: The four parameter Exponentiated Generalized Gamma...

In ousuga/RelDists: Estimation for some Reliability Distributions

The four parameter Exponentiated Generalized Gamma distribution

Description

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.

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.

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.

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

cordeiro2011RelDists

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

ousuga/RelDists documentation built on July 10, 2024, 12:48 p.m.