Newdistns (version 1.0)

gepg: Geometric exponential Poisson G distribution

Description

Computes the pdf, cdf, quantile and random numbers of the geometric exponential Poisson G distribution due to Nadarajah et al. (2013) specified by the pdf $$f (x) = \displaystyle \frac {\displaystyle \theta (1 - \eta) \left[ 1 - \exp (-\theta) \right] g (x) \exp \left[ -\theta + \theta G (x) \right]}{\displaystyle \left{ 1 - \exp (-\theta) - \eta + \eta \exp \left[ -\theta + \theta G (x) \right] \right}^2}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $\theta > 0$, the first scale parameter, and $0 < eta < 1$, the second scale parameter.

Usage

dgepg(x, spec, theta = 1, eta = 0.5, log = FALSE, ...)
pgepg(x, spec, theta = 1, eta = 0.5, log.p = FALSE, lower.tail = TRUE, ...)
qgepg(p, spec, theta = 1, eta = 0.5, log.p = FALSE, lower.tail = TRUE, ...)
rgepg(n, spec, theta = 1, eta = 0.5, ...)

Arguments

x

scaler or vector of values at which the pdf or cdf needs to be computed

p

scaler or vector of values at which the quantile needs to be computed

n

number of random numbers to be generated

theta

the value of first scale parameter, must be positive, the default is 1

eta

the value of second scale parameter, must be in the open unit interval, the default is 0.5

spec

a character string specifying the distribution of G and g (for example, "norm" if G and g correspond to the standard normal).

log

if TRUE then log(pdf) are returned

log.p

if TRUE then log(cdf) are returned and quantiles are computed for exp(p)

lower.tail

if FALSE then 1-cdf are returned and quantiles are computed for 1-p

...

other parameters

Value

• An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the quantile values computed at p or an object of the same length as n, giving the random numbers generated.

References

S. Nadarajah, Newdistns: An R Package for new families of distributions, submitted S. Nadarajah, V. G. Cancho, E. M. M. Ortega, The geometric exponential Poisson distribution, Stat Methods Appl 22 (2013) 355-380

Examples

x=runif(10,min=0,max=1)
dgepg(x,"exp",theta=1,eta=0.5)
pgepg(x,"exp",theta=1,eta=0.5)
qgepg(x,"exp",theta=1,eta=0.5)
rgepg(10,"exp",theta=1,eta=0.5)