The Extended Exponential Geometric distribution

Density, distribution function, quantile function, random generation and hazard function for the Extended Exponential Geometric distribution with parameters mu and sigma.

Usage

dEEG(x, mu, sigma, log = FALSE)

pEEG(q, mu, sigma, lower.tail = TRUE, log.p = FALSE)

qEEG(p, mu, sigma, lower.tail = TRUE, log.p = FALSE)

rEEG(n, mu, sigma)

hEEG(x, mu, sigma)

Arguments

x, q: vector of quantiles.
mu: parameter.
sigma: 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

dEEG gives the density, pEEG gives the distribution function, qEEG gives the quantile function, rEEG generates random deviates and hEEG gives the hazard function.

Details

The Extended Exponential Geometric distribution with parameters mu, and sigmahas density given by

\(f(x)= \mu \sigma \exp(-\mu x)(1 - (1 - \sigma)\exp(-\mu x))^{-2},\)

for \(x > 0\), \(\mu > 0\) and \(\sigma > 0\).

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 .

Adamidis K, Dimitrakopoulou T, Loukas S (2005). “On an extension of the exponential-geometric distribution.” Statistics & probability letters, 73(3), 259–269.

Author

Johan David Marin Benjumea, johand.marin@udea.edu.co

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function 
par(mfrow=c(1,1))
curve(dEEG(x, mu = 1, sigma =3), from = 0, to = 10, 
      col = "red", las = 1, ylab = "f(x)")


## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pEEG(x, mu = 1, sigma =3), from = 0, to = 10, 
      ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)")
curve(pEEG(x, mu = 1, sigma =3, lower.tail = FALSE), 
      from = 0, to = 6, 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 = qEEG(p = p, mu = 1, sigma =0.5), y = p, 
     xlab = "Quantile", las = 1, ylab = "Probability")
curve(pEEG(x, mu = 1, sigma =0.5), from = 0, add = TRUE, 
      col = "red")

## The random function
hist(rEEG(1000, mu = 1, sigma =1), freq = FALSE, xlab = "x", 
     ylim = c(0, 0.9), las = 1, main = "")
curve(dEEG(x, mu = 1, sigma =1),  from = 0, add = TRUE, 
      col = "red", ylim = c(0, 0.8))


## The Hazard function
par(mfrow=c(1,1))
curve(hEEG(x, mu = 1, sigma =0.5), from = 0, to = 2, 
      col = "red", ylab = "Hazard function", las = 1)


par(old_par) # restore previous graphical parameters