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The Weighted Generalized Exponential-Exponential distribution

Source: R/dWGEE.R
dWGEE.Rd

Density, distribution function, quantile function, random generation and hazard function for the Weighted Generalized Exponential-Exponential distribution with parameters mu, sigma and nu.

Usage

dWGEE(x, mu, sigma, nu, log = FALSE)

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

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

rWGEE(n, mu, sigma, nu)

hWGEE(x, mu, sigma, nu)

Arguments

x, q

vector of quantiles.

mu

parameter.

sigma

parameter.

nu

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

dWGEE gives the density, pWGEE gives the distribution function, qWGEE gives the quantile function, rWGEE generates random deviates and hWGEE gives the hazard function.

Details

The Weighted Generalized Exponential-Exponential Distribution with parameters mu, sigma and nu has density given by

\(f(x)= \sigma \nu \exp(-\nu x) (1 - \exp(-\nu x))^{\sigma - 1} (1 - \exp(-\mu \nu x)) / 1 - \sigma B(\mu + 1, \sigma),\)

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

References

Mahdavi A (2015). “Two Weighted Distributions Generated by Exponential Distribution.” Journal of Mathematical Extension, 9(1), 1–12.

Mahdavi A (2015). “Two weighted distributions generated by exponential distribution.” Journal of Mathematical Extension, 9, 1–12.

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 
curve(dWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, to = 6, 
ylim = c(0, 1), col = "red", las = 1, ylab = "The probability density function")


## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, to = 6, 
ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pWGEE(x, mu = 5, sigma = 0.5, nu = 1, lower.tail = FALSE), 
from = 0, to = 6, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")


## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qWGEE(p = p, mu = 5, sigma = 0.5, nu = 1), y = p, 
xlab = "Quantile", las = 1, ylab = "Probability")
curve(pWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, add = TRUE, 
col = "red")

## The random function
hist(rWGEE(1000, mu = 5, sigma = 0.5, nu = 1), freq = FALSE, xlab = "x", 
ylim = c(0, 1), las = 1, main = "")
curve(dWGEE(x, mu = 5, sigma = 0.5, nu = 1),  from = 0, add = TRUE, 
col = "red", ylim = c(0, 1))


## The Hazard function(
par(mfrow=c(1,1))
curve(hWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, to = 6, 
ylim = c(0, 1.4), col = "red", ylab = "The hazard function", las = 1)


par(old_par) # restore previous graphical parameters