distribution of "signed rank" in Wilcoxon's test

sim_signedrank.r

library(ggplot2)


out <- vector("list", 10000)
for(i in 1:10000){
  x <- rt(10,3)
  out[[i]] <- sign(x)*rank(abs(x))  
}

ggplot(data=NULL)+
  geom_bar(aes(x=unlist(out), y=after_stat(count/sum(count))))+
  theme_bw()+labs(x="signed ranked")

ggsave("symmetry_sr.png")

out2 <- vector("list", 10000)
for(i in 1:10000){
  x <- rweibull(10,1.5) - log(2)^(1/1.5)
  out2[[i]] <- sign(x)*rank(abs(x))  
}

ggplot(data=NULL)+
  geom_bar(aes(x=unlist(out2), y=after_stat(count/sum(count))))+
  theme_bw()+labs(x="signed ranked")


ggsave("asymmetry_sr.png")