RelDists (version 1.0.0)

dEEG: The Extended Exponential Geometric distribution

Description

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)

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.

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.

Author

Johan David Marin Benjumea,

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

almalki2014modificationsRelDists

adamidis2005extensionRelDists

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