dWGEE | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Weighted Generalized Exponential-Exponential distribution
with parameters mu
, sigma
and nu
.
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)
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. |
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
.
dWGEE
gives the density, pWGEE
gives the distribution
function, qWGEE
gives the quantile function, rWGEE
generates random deviates and hWGEE
gives the hazard function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
Mahdavi2015RelDists
\insertRefmahdavi2015twoRelDists
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
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