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