Newdistns (version 1.0)

gammag1: Gamma G distribution due to Zografos and Balakrishnan (2009)

Description

Computes the pdf, cdf, quantile and random numbers of the gamma G distribution due to Zografos and Balakrishnan (2009) specified by the pdf $$f (x) = \frac{\displaystyle 1}{\displaystyle \Gamma(a)} g (x) \left{ -\log \left[ 1 - G(x) \right] \right}^{a-1}$$ for $G$ any valid cdf, $g$ the corresponding pdf, and $a > 0$, the shape parameter.

Usage

dgammag1(x, spec, a = 1, log = FALSE, ...)
pgammag1(x, spec, a = 1, log.p = FALSE, lower.tail = TRUE, ...)
qgammag1(p, spec, a = 1, log.p = FALSE, lower.tail = TRUE, ...)
rgammag1(n, spec, a = 1, ...)

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

a

the value of the shape parameter, must be positive, the default is 1

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 K. Zografos, N. Balakrishnan, On families of beta- and generalized gamma-generated distributions and associated inference, Statistical Methodology 6 (2009) 344-362

Examples

x=runif(10,min=0,max=1)
dgammag1(x,"exp",a=1)
pgammag1(x,"exp",a=1)
qgammag1(x,"exp",a=1)
rgammag1(10,"exp",a=1)