2017-10-18 untitled from rstudio

untitled-2017-10-18.R

library(plyr)

set.seed(2017-06-08)

l=0.5

# this distribution has mean and variance both = l above
# importantly it never produces values < 0
plot(table(rpois(100, lambda=l)))


asymptotic_v_actual <- function(sample_size) {
  means <- raply(100000, mean(rpois(sample_size, lambda=l)))
  hist(means, prob=T, col="grey", border = NA,
       main=paste0("sample size=", as.character(sample_size)))
  curve(dnorm(x, mean=l, sd=sqrt(l/sample_size)), add=T, lwd=2, col="red")
}

asymptotic_v_actual(sample_size=5)

asymptotic_v_actual(sample_size=10)

asymptotic_v_actual(sample_size=100)

asymptotic_v_actual(sample_size=1000)


# probability of x < 0 for different sample sizes:
sizes <- 1:20
plot(sizes, pnorm(0, mean=l, sd=sqrt(l/sizes)), type="o", 
     main="p(x < 0) for different sample size")