dQXGP function

The Quasi XGamma Poisson distribution

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)

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.

Returns

dQXGP gives the density, pQXGP gives the distribution function, qQXGP gives the quantile function, rQXGP

generates random deviates and hQXGP gives the hazard function.

Details

The Quasi XGamma Poisson distribution with parameters mu, sigma and nu has density given by:

c("$f(x)= K(\\mu, \\sigma, \\nu)(\\frac {\\sigma^{2} x^{2}}{2} + \\mu)\n$", "$exp(\\frac{\\nu exp(-\\sigma x)(1 + \\mu + \\sigma x + \\frac {\\sigma^{2}x^{2}}{2})}{1+\\mu} - \\sigma x),$")

for $x > 0$, $\mu> 0$, $\sigma> 0$, $\nu> 1$.

where

$K(\mu, \sigma, \nu) = \frac{\nu \sigma}{(exp(\nu)-1)(1+\mu)}$

Examples

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

References

Rdpack::insert_ref(key="subhradev2018",package="RelDists")

Author(s)

Simon Zapata