順序統計量とBeta分布

beta.py

import numpy as np
import matplotlib.pyplot as plt

print(np.random.rand(10))

def ord_sampling(N,n,p):
    sample = np.random.rand(N,n)
    sample_ord = np.sort(sample, axis=1)[:,p-1]
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    ax.hist(sample_ord, bins=30)
    fig.show()
    
N = int(1e+5)

n = 10
p = 3
ord_sampling(N,n,p)

def compare(N, n, p, fun):
    sample = np.random.rand(N,n)
    sample_ord = np.sort(sample, axis=1)[:,p-1]
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    x = np.linspace(0,1,100)
    ax.plot(x, fun(x))
    ax.hist(sample_ord, bins=30, density=True)
    fig.show()
    
n = 2
p = 1
fun = lambda x : 2 - 2 * x
compare(N, n, p, fun)

beta.R

library(dplyr)
library(ggplot2)

set.seed(123)
runif(10)
runif(10)

ord_sampling <- function(N,n,p){
  x <- c()
  for(i in 1:N){
    x[i] <- sort(runif(n))[p]
  }
  data.frame(x=x) %>%
    ggplot(aes(x=x)) +
    geom_histogram(binwidth = 0.05,
                   boundary = 0,
                   fill = "royal blue") +
    labs(title = paste("n =",as.character(n),", p = ",as.character(p)))
}

N <- 1e+5

n <- 10
p <- 3
ord_sampling(N,n,p)

n <- 10
p <- 1
ord_sampling(N,n,p)

n <- 10
p <- 2
ord_sampling(N,n,p)

n <- 10
p <- 4
ord_sampling(N,n,p)

n <- 10
p <- 5
ord_sampling(N,n,p)

compare <- function(N,n,p,fun){
  x <- c()
  for(i in 1:N){
    x[i] <- sort(runif(n))[p]
  }
  data.frame(x=x) %>%
    ggplot(aes(x=x)) +
    geom_histogram(aes(y=..density..),
                   fill = 'royal blue',
                   binwidth = 0.05,
                   boundary = 0) +
    stat_function(fun=fun) +
    labs(title = paste("n =",as.character(n),", p = ",as.character(p)))
}

N <- 1e+5
n <- 2
p <- 1
fun <- function(x) 2*(1-x)
compare(N,n,p,fun)