• Licenza: Gnu FDL
• funzione di densità di probabilità della variabile casuale di Kumaraswamy

Kumaraswamy

Script in R

dkuma <- function(x,a,b){     return(a*b*x^(a-1)*(1-x^a)^(b-1))}
modakuma <- function(a,b){return(max(0,min(1,((a-1)/(a*b-1))^(1/a))))}

dx <- 0.001;
x <- seq(dx/1000,1-dx/1000,dx)

a <-  c(0.5,1,0.5,1.5,1.5,2,2,5)
b <- c(0.5,1,1.5,1,1.5,2,5,2)

maxy<-0
i<-seq(1,length(a));
for(ii in i) {maxy<-min(10,max(maxy,dkuma(modakuma(a[ii],b[ii]),a[ii],b[ii])))}

png("C:/temp/Grafico_v.c._Kumaraswamy.png",width=800,heigh=600)
plot(x,dkuma(x,a[1],b[1]),
     type='l',
     axes=FALSE,xlab=NA,ylab=NA,
     ylim=c(0,maxy), xlim=c(0,1),
     main="v.c. di Kumaraswamy");
abline(0,0);lines(c(0,0),c(-10,100))
for(ii in i){lines(x,dkuma(x,a[ii],b[ii]),col=ii)}
legend(0.45,maxy,col=i,legend=paste("a =",a,"  b =",b),lty=1,bty='n')
text(0,1,"1",adj=1.4)
text(1,0,"1",adj=c(0.5,1.4))
dev.off();