Newdistns (version 1.0)

kumg: Kumaraswamy G distribution

Description

Computes the pdf, cdf, quantile and random numbers of the Kumaraswamy G distribution due to Cordeiro and Castro (2011) specified by the pdf $$f (x) = a b g (x) G^{a - 1} (x) \left[ 1 - G^a (x) \right]^{b - 1}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $a > 0$, the first shape parameter, and $b > 0$, the second shape parameter.

Usage

dkumg(x, spec, a = 1, b = 1, log = FALSE, ...)
pkumg(x, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qkumg(p, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rkumg(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 G. M. Cordeiro, M. Castro, A new family of generalized distributions, Journal of Statistical Computation and Simulation 81 (2011) 883-898

Examples

x=runif(10,min=0,max=1)
dkumg(x,"exp",a=1,b=1)
pkumg(x,"exp",a=1,b=1)
qkumg(x,"exp",a=1,b=1)
rkumg(10,"exp",a=1,b=1)