dWP {RelDists} | R Documentation |
The Weibull Poisson distribution
Description
Density, distribution function, quantile function,
random generation and hazard function for the Weibull Poisson distribution
with parameters mu
, sigma
and nu
.
Usage
dWP(x, mu, sigma, nu, log = FALSE)
pWP(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
qWP(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
rWP(n, mu, sigma, nu)
hWP(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. |
Details
The Weibull Poisson distribution with parameters mu
,
sigma
and nu
has density given by
f(x) = \frac{\mu \sigma \nu e^{-\nu}} {1-e^{-\nu}} x^{\mu-1} exp({-\sigma x^{\mu}+\nu exp({-\sigma} x^{\mu}) }),
for x > 0.
Value
dWP
gives the density, pWP
gives the distribution
function, qWP
gives the quantile function, rWP
generates random deviates and hWP
gives the hazard function.
Author(s)
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
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.
Wanbo L, Daimin S (1967). “A new compounding life distribution: the Weibull–Poisson distribution.” Journal of Applied Statistics, 9(1), 21–38. doi:10.1080/02664763.2011.575126, https://doi.org/10.1080/02664763.2011.575126.
Examples
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters
## The probability density function
curve(dWP(x, mu=1.5, sigma=0.5, nu=10), from=0.0001, to=2,
col="red", las=1, ylab="f(x)")
## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pWP(x, mu=1.5, sigma=0.5, nu=10),
from=0.0001, to=2, col="red", las=1, ylab="F(x)")
curve(pWP(x, mu=1.5, sigma=0.5, nu=10, lower.tail=FALSE),
from=0.0001, to=2, col="red", las=1, ylab="R(x)")
## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qWP(p, mu=1.5, sigma=0.5, nu=10), y=p, xlab="Quantile",
las=1, ylab="Probability")
curve(pWP(x, mu=1.5, sigma=0.5, nu=10),
from=0, add=TRUE, col="red")
## The random function
hist(rWP(n=10000, mu=1.5, sigma=0.5, nu=10), freq=FALSE,
xlab="x", ylim=c(0, 2.2), las=1, main="")
curve(dWP(x, mu=1.5, sigma=0.5, nu=10),
from=0.001, to=4, add=TRUE, col="red")
## The Hazard function
curve(hWP(x, mu=1.5, sigma=0.5, nu=10), from=0.001, to=5,
col="red", ylab="Hazard function", las=1)
par(old_par) # restore previous graphical parameters