simulation study for wilcox.test

wilcox.r

library(ggplot2)
#check the moments
integrate(function(x)x*dexp(x), 0,Inf)
integrate(function(x)x^2*dexp(x), 0,Inf)
integrate(function(x)x*dnorm(x,1,1), -Inf,Inf)
integrate(function(x)x^2*dnorm(x,1,1), -Inf,Inf)


pv_simfun <- function(n1,n2){
  x1 <- rexp(n1)
  x2 <- rnorm(n2,1,1)
  pw <- wilcox.test(x1,x2)$p.value
  pt <- t.test(x1,x2)$p.value
  data.frame(p=c(pw,pt), method=c("wilxcox","t"))
}


res <- lapply(1:10000, 
              function(i){set.seed(i);pv_simfun(100,100)})
res <- do.call("rbind",res)

ggplot(res,aes(x=p, colour=method, group=method, linetype = method))+
  stat_ecdf()+
  scale_color_brewer(palette = "Set1")+
  theme_bw()+labs(x="nominal", y="actual")
ggsave("wil_p.png")

ggplot(data = NULL)+
  stat_function(fun=dexp, aes(colour="exp"))+
  stat_function(fun=dnorm, aes(colour="normal"), args = list(mean=1))+
  theme_bw()+xlim(c(-4,4))+labs(colour="pop. dist.", y="density")

ggsave("pop_dens.png")