dQXGP | R Documentation |
Density, distribution function,quantile function,
random generation and hazard function for the Quasi XGamma Poisson distribution
with parameters mu
, sigma
and nu
.
dQXGP(x, mu, sigma, nu, log = FALSE) pQXGP(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qQXGP(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rQXGP(n, mu, sigma, nu) hQXGP(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 Quasi XGamma Poisson distribution with parameters mu
,
sigma
and nu
has density given by:
f(x)= K(μ, σ, ν)(\frac {σ^{2} x^{2}}{2} + μ) exp(\frac{ν exp(-σ x)(1 + μ + σ x + \frac {σ^{2}x^{2}}{2})}{1+μ} - σ x),
for x > 0, μ> 0, σ> 0, ν> 1.
where
K(μ, σ, ν) = \frac{ν σ}{(exp(ν)-1)(1+μ)}
dQXGP
gives the density, pQXGP
gives the distribution
function, qQXGP
gives the quantile function, rQXGP
generates random deviates and hQXGP
gives the hazard function.
Simon Zapata
subhradev2018RelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function curve(dQXGP(x, mu=0.5, sigma=1, nu=1), from=0.1, to=8, ylim=c(0, 0.6), col="red", las=1, ylab="f(x)") ## The cumulative distribution and the Reliability function par(mfrow=c(1, 2)) curve(pQXGP(x, mu=0.5, sigma=1, nu=1), from=0.1, to=8, col="red", las=1, ylab="F(x)") curve(pQXGP(x, mu=0.5, sigma=1, nu=1, lower.tail=FALSE), from=0.1, to=8, col="red", las=1, ylab="R(x)") ## The quantile function p <- seq(from=0, to=0.99999, length.out=100) plot(x=qQXGP(p, mu=0.5, sigma=1, nu=1), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pQXGP(x, mu=0.5, sigma=1, nu=1), from=0.1, add=TRUE, col="red") ## The random function hist(rQXGP(n=1000, mu=0.5, sigma=1, nu=1), freq=FALSE, xlab="x", ylim=c(0, 0.4), las=1, main="", xlim=c(0, 15)) curve(dQXGP(x, mu=0.5, sigma=1, nu=1), from=0.001, to=500, add=TRUE, col="red") ## The Hazard function curve(hQXGP(x, mu=0.5, sigma=1, nu=1), from=0.01, to=3, col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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