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