Exponentiated Weibull Distribution

Question

I'm trying to understand Exponentiated Weibull (EW) function ExpoWeibull from package reliaR , however the function only use a single shape parameter and a scale parameter. From what I've read about the EW distribution, a second shape parameter is used. Is there an existing implementation of EW for R, that accepts two shape parameters? If not, how does one go about implementing the distribution function?

Answer 1

I disagree with Brad. The function computed in the reliaR package is correct. It's just the same formula like on Wikipedia. You'll just have to substitute (x/lambda)=x1, k=alpha1 and Alpha=Theta. Just take the cumulative distribution, substitute the 3 variables and derive it! Don't Forget to Substitute dx too! Or have a look at http://www.academia.edu/6178638/Estimation_for_the_Parameters_of_the_Exponentiated_Weibull_Distribution_Based_on_Progressive_Hybrid_Censored_Samples. Page 1714 There you can see: both cumulative function are equal

Answer 2

As far as I can tell, the function in that package is wrong. I had to code the distribution myself. If lambda is the scale parameter and x and alpha are the shape parameters (going by the notation in Wikipedia for simplicity):

dexpweib=function(x, alpha, k, lambda, log=FALSE){
if ((!is.numeric(x)) || (!is.numeric(alpha))|| (!is.numeric(k)) || (!is.numeric(lambda))){ 
    stop("non-numeric argument to mathematical function")}
if((length(alpha)!= 1) || (length(k)!=1) || (length(lambda)!=1)){
    stop("Non-x parameters must be atomic")}
if ((min(x) <= 0) || (alpha <= 0) || (k <= 0) || (lambda <= 0)){ 
    stop("Invalid arguments. Must be > 0 ")}
u <- exp(-(x/lambda)^k)
pdf <- ((alpha*k)/(lambda^k))*(x^(k-1))*u*((1-u)^(alpha-1))
if (log) 
    pdf <- log(pdf)
return(pdf)

}

pexpweib=function(q, alpha, k, lambda, log.p=FALSE){
if ((!is.numeric(q)) || (!is.numeric(alpha))|| (!is.numeric(k)) || (!is.numeric(lambda))){ 
    stop("non-numeric argument to mathematical function")}
if((length(alpha)!= 1) || (length(k)!=1) || (length(lambda)!=1)){
    stop("Non-q parameters must be atomic")}
if ((min(q) <= 0) || (alpha <= 0) || (k <= 0) || (lambda <= 0)){ 
    stop("Invalid arguments. Must be > 0 ")}
u <- exp(-(q/lambda)^k)
cdf <- (1-u)^alpha
if (log.p) 
    cdf <- log(cdf)
return(cdf)

}