AdequacyModel (version 1.0.1)

kwp: Pseudo-Random Numbers - Kumaraswamy Pareto

Description

Generates pseudorandom numbers from Kumaraswamy Pareto Distribution.

Usage

rkwp(n, k, beta, a, b)

Arguments

n

Amount of generated numbers;

k

Shape parameter of the Kumaraswamy Pareto distribution;

beta

Scale parameter Kumaraswamy Pareto distribution;

a

Shape parameter Kumaraswamy Pareto distribution;

b

Shape parameter Kumaraswamy Pareto distribution.

Details

The Kw-P (Kumaraswamy Pareto) distribution is not in fact very tractable. However, its heavy tail can adjust skewed data that cannot be properly fitted by existing distributions. Furthermore, the cumulative and hazard rate functions are simple. The Pareto distribution function Kumaraswamy function is given by

$$F(x; \beta, k, a, b) = 1 - \left{1 - \left[1 - \left(\frac{\beta}{x}\right)^k\right]^a\right}^b,$$ where $\beta>0$ ($x>=\beta$) is a scale parameter and the other positive parameters $k$, $a$ and $b$ are shape parameters.

References

Bourguinon, M.; Silva, R.B.; Zea, L.M. and Cordeiro, G.M. (2013). The Kumaraswamy Pareto distribution. Journal of Statistical Theory and Applications 12, 129-144.

See Also

rweibull

Examples

beta = 1.5
k = 1.5
a = 1.5
b = 3.5

x<-seq(beta, 10, 0.01)

pdfKWP <- function(k,bet,a,b,x){
a*b*k*bet^(k)*(1-(beta/x)^k)^(a-1)*(1-(1-(beta/x)^k)^(a))^(b-1)/x^(k+1)
}

hist(rkwp(100,k,beta,a,b), freq = FALSE,main="",xlab="x",
     ylab="Density",xlim=c(1.5,7),ylim=c(0,1.5),lwd=1)
lines(x,pdfKWP(k,beta,a,b,x),lty=1,col="black",
      lwd=1,type="l",xlim=c(1.5,7),ylim=c(0,1.5))
box()