中心極限定理

// 依存関係のインストール

:dep image = "0.23"
:dep evcxr_image = "1.1"

// プロット用ライブラリ
:dep plotters = { version = "^0.3.5", default_features = false, features = ["evcxr", "all_series", "all_elements"] }

// 乱数
:dep rand = { version = "0.8.5" }

// ライブラリ
:dep myml = { path = "../myml/" }

// インポート
use evcxr_image::ImageDisplay;
use image::{GenericImage, imageops::FilterType};

use plotters::prelude::*;
use rand::prelude::*;

use myml::{utility::linspace, normal::normal};

サンプリング

/// ランダムな変数`n`個を`rep`回サンプリングする
fn sample_means(n: usize, rep: usize) -> Vec<f64> {
    (0..rep)
        .map(|_| {
            // 平均
            let mean = (0..n)
                .map(|_| random::<f64>())
                .sum::<f64>() / n as f64;
            mean
        })
        .collect()
}

const REP: usize = 10000;

\(N = 1\) のとき

let means = sample_means(1, REP);

evcxr_figure((640, 480), |root| {
    root.fill(&WHITE)?;

    let mut chart = ChartBuilder::on(&root)
        .caption("N = 1", ("Sans", 20).into_font())
        .x_label_area_size(50)
        .y_label_area_size(50)
        .build_cartesian_2d(0..10, 0.0..40.0)?;

    chart.configure_mesh()
        .draw()?;

    let hist = Histogram::vertical(&chart)
        .style(BLUE.filled())
        .margin(10)
        .data(means.iter().map(|&x| ((x * 10.0) as i32, 0.01)));

    chart.draw_series(hist)?;
    
    Ok(())
})

\(N = 2\) のとき

let means = sample_means(2, REP);

evcxr_figure((640, 480), |root| {
    root.fill(&WHITE)?;

    let mut chart = ChartBuilder::on(&root)
        .caption("N = 2", ("Sans", 20).into_font())
        .x_label_area_size(50)
        .y_label_area_size(50)
        .build_cartesian_2d(0..10, 0.0..40.0)?;

    chart.configure_mesh()
        .draw()?;

    let hist = Histogram::vertical(&chart)
        .style(BLUE.filled())
        .margin(10)
        .data(means.iter().map(|&x| ((x * 10.0) as i32, 0.01)));

    chart.draw_series(hist)?;
    
    Ok(())
})

\(N = 4\) のとき

let means = sample_means(4, REP);

evcxr_figure((640, 480), |root| {
    root.fill(&WHITE)?;

    let mut chart = ChartBuilder::on(&root)
        .caption("N = 4", ("Sans", 20).into_font())
        .x_label_area_size(50)
        .y_label_area_size(50)
        .build_cartesian_2d(0..10, 0.0..40.0)?;

    chart.configure_mesh()
        .draw()?;

    let hist = Histogram::vertical(&chart)
        .style(BLUE.filled())
        .margin(10)
        .data(means.iter().map(|&x| ((x * 10.0) as i32, 0.01)));

    chart.draw_series(hist)?;
    
    Ok(())
})

\(N = 10\) のとき

let means = sample_means(10, REP);

evcxr_figure((640, 480), |root| {
    root.fill(&WHITE)?;

    let mut chart = ChartBuilder::on(&root)
        .caption("N = 10", ("Sans", 20).into_font())
        .x_label_area_size(50)
        .y_label_area_size(50)
        .build_cartesian_2d(0..20, 0.0..40.0)?;

    chart.configure_mesh()
        .draw()?;

    let hist = Histogram::vertical(&chart)
        .style(BLUE.filled())
        .margin(5)
        .data(means.iter().map(|&x| ((x * 20.0) as i32, 0.01)));

    chart.draw_series(hist)?;
    
    Ok(())
})