標本平均と標本中央値の比較

compare_mean_median.py

import numpy as np
import matplotlib.pyplot as plt

def compare(N, n, p, rng):
    sample = rng(N,n)
    sample_mea = np.mean(sample, axis=1)
    sample_med = np.sort(sample, axis=1)[:,p]
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    ax.hist(sample_mea, bins=50, normed=True, alpha = 0.5)
    ax.hist(sample_med, bins=50, normed=True, alpha = 0.5)
    fig.show()
    
N = int(1e+5)
n = 1001 #奇数にする
p = n // 2 + 1
rng = np.random.rand
#dist = np.random.random
#dist = np.random.exponential
compare(N,n,p,rng)

compare_mean_median.R

library(dplyr)
library(ggplot2)

compare <- function(N,n,p,dist){
  rng <- get(dist)
  sample.med <- c()
  sample.mea <- c()
  for(i in 1:N){
    sample <- rng(n)
    sample.med[i] <- sort(sample)[p]
    sample.mea[i] <- mean(sample)
    }
  data.frame(mean = sample.mea, median = sample.med) %>%
    tidyr::gather() %>%
    ggplot(aes(x=value, fill=key)) +
    geom_histogram(position = "identity", alpha = 0.6) +
    labs(title = paste(dist,"n =",as.character(n)))
}


N <- 1e+5
n <- 1001 #奇数にする
p <- ceiling(n/2)
dist <- "rnorm"
compare(N,n,p,dist)