dWP | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Weibull Poisson distribution
with parameters mu
, sigma
and nu
.
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)
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 Weibull Poisson distribution with parameters mu
,
sigma
and nu
has density given by
f(x) = \frac{μ σ ν e^{-ν}} {1-e^{-ν}} x^{μ-1} exp({-σ x^{μ}+ν exp({-σ} x^{μ}) }),
for x > 0.
dWP
gives the density, pWP
gives the distribution
function, qWP
gives the quantile function, rWP
generates random deviates and hWP
gives the hazard function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefWanbo2012RelDists
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
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