Newdistns (version 1.0)

gbg: Generalized beta G distribution

Description

Computes the pdf, cdf, quantile and random numbers of the generalized beta G distribution due to Alexander et al. (2012) specified by the pdf $$f (x) = \frac {c}{B (a, b)} g (x) G^{a c - 1} (x) \left[ 1 - G^c (x) \right]^{b - 1}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $a > 0$, the first shape parameter, $b > 0$, the second shape parameter and $c > 0$, the third shape parameter.

Usage

dgbg(x, spec, a = 1, b = 1, c = 1, log = FALSE, ...)
pgbg(x, spec, a = 1, b = 1, c = 1, log.p = FALSE, lower.tail = TRUE, ...)
qgbg(p, spec, a = 1, b = 1, c = 1, log.p = FALSE, lower.tail = TRUE, ...)
rgbg(n, spec, a = 1, b = 1, c = 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

c

the value of the third 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 C. Alexander, G. M. Cordeiro, E. M. M. Ortega, Generalized beta-generated distributions, Computational Statistics and Data Analysis 56 (2012) 1880-1897

Examples

x=runif(10,min=0,max=1)
dgbg(x,"exp",a=1,b=1,c=1)
pgbg(x,"exp",a=1,b=1,c=1)
qgbg(x,"exp",a=1,b=1,c=1)
rgbg(10,"exp",a=1,b=1,c=1)