Newdistns (version 1.0)

betag: Beta G distribution

Description

Computes the pdf, cdf, quantile and random numbers of the beta G distribution due to Eugene et al. (2002) specified by the pdf $$f (x) = \frac {\displaystyle 1}{\displaystyle B(a,b)} g(x)\left[ G(x) \right]^{a - 1} \left[ 1 - G(x) \right]^{b - 1}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $a > 0$, the first shape parameter, and $b > 0$, the second shape parameter.

Usage

dbetag(x, spec, a = 1, b = 1, log = FALSE, ...)
pbetag(x, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qbetag(p, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rbetag(n, spec, a = 1, b = 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 first shape parameter, must be positive, the default is 1

b

the value of the second 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 N. Eugene, C. Lee, F. Famoye, Beta-normal distribution and its applications, Communications in Statistics---Theory and Methods, 31 (2002) 497-512

Examples

x=runif(10,min=0,max=1)
dbetag(x,"exp",a=1,b=1)
pbetag(x,"exp",a=1,b=1)
qbetag(x,"exp",a=1,b=1)
rbetag(10,"exp",a=1,b=1)