Newdistns (version 1.0)

beg: Beta extended G distribution

Description

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

Usage

dbeg(x, spec, alpha = 1, a = 1, b = 1, log = FALSE, ...)
pbeg(x, spec, alpha = 1, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qbeg(p, spec, alpha = 1, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rbeg(n, spec, alpha = 1, 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

alpha

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

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 G. M. Cordeiro, E. M. M. Ortega, G. Silva, The beta extended Weibull family, Journal of Probability and Statistical Science 10 (2012) 15-40

Examples

x=runif(10,min=0,max=1)
dbeg(x,"exp",alpha=1,a=1,b=1)
pbeg(x,"exp",alpha=1,a=1,b=1)
qbeg(x,"exp",alpha=1,a=1,b=1)
rbeg(10,"exp",alpha=1,a=1,b=1)