Histograms and Empirical Distribution Functions

/**
 * Fintech Math Bootcamp · Lesson 039 of 120
 * Histograms and Empirical Distribution Functions
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A histogram changes with bins; an ECDF preserves sample order
 * Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
 *
 * Try it:   Where does 9 go with these half-open bins?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson039() {
  const x = [1,2,2,4,9];
  const edges = [0,3,6,9,12];
  const counts = edges.slice(0,-1).map((lo,i) =>
    x.filter(v => v>=lo && v<edges[i+1]).length);
  const ecdfAt2 = x.filter(v=>v<=2).length/x.length;
  const result = {counts, ecdfAt2};
  return result;
}

export const checkedResult = {"counts":[3,1,0,1],"ecdfAt2":0.6};

// Run this file directly: npx tsx lessons/04-location-ranking-and-exploratory-summaries/039-histograms-and-empirical-distribution-functions.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson039(), null, 2));
}

# Fintech Math Bootcamp · Lesson 039 of 120
# Histograms and Empirical Distribution Functions
# Module 04: Location, Ranking, and Exploratory Summaries
#
# Scenario: A histogram changes with bins; an ECDF preserves sample order
# Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
#
# Try it:   Where does 9 go with these half-open bins?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json


def lesson039() -> dict:
    x = [1, 2, 2, 4, 9]
    edges = [0, 3, 6, 9, 12]
    # Half-open bins [lo, hi): a value on an edge goes to the bin that starts there.
    counts = [sum(1 for v in x if lo <= v < hi) for lo, hi in zip(edges, edges[1:])]
    ecdf_at_2 = sum(1 for v in x if v <= 2) / len(x)
    return {"counts": counts, "ecdfAt2": ecdf_at_2}


if __name__ == "__main__":
    print(json.dumps(lesson039(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 039 of 120
 * Histograms and Empirical Distribution Functions
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A histogram changes with bins; an ECDF preserves sample order
 * Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
 *
 * Try it:   Where does 9 go with these half-open bins?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

import java.util.ArrayList;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;

public class Main {
    static Map<String, Object> lesson039() {
        double[] x = {1, 2, 2, 4, 9};
        double[] edges = {0, 3, 6, 9, 12};
        // Half-open bins [lo, hi): a value on an edge goes to the bin that starts there.
        List<Integer> counts = new ArrayList<Integer>();
        for (int i = 0; i + 1 < edges.length; i++) {
            int count = 0;
            for (double v : x) if (v >= edges[i] && v < edges[i + 1]) count++;
            counts.add(count);
        }
        int atOrBelow2 = 0;
        for (double v : x) if (v <= 2) atOrBelow2++;

        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("counts", counts);
        result.put("ecdfAt2", (double) atOrBelow2 / x.length);
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson039(), ""));
    }

    // --- Minimal JSON printer: maps keep insertion order, 2-space indent. ---

    static String toJson(Object value, String indent) {
        if (value == null) return "null";
        if (value instanceof String) return "\"" + value + "\"";
        if (value instanceof Double) return formatNumber((Double) value);
        if (value instanceof Number) return value.toString();
        if (value instanceof double[]) {
            List<Object> items = new ArrayList<Object>();
            for (double v : (double[]) value) items.add(v);
            return toJson(items, indent);
        }
        String inner = indent + "  ";
        StringBuilder sb = new StringBuilder();
        if (value instanceof Map) {
            Map<?, ?> map = (Map<?, ?>) value;
            if (map.isEmpty()) return "{}";
            sb.append("{\n");
            int i = 0;
            for (Map.Entry<?, ?> entry : map.entrySet()) {
                sb.append(inner).append('"').append(entry.getKey()).append("\": ")
                  .append(toJson(entry.getValue(), inner))
                  .append(++i < map.size() ? ",\n" : "\n");
            }
            return sb.append(indent).append('}').toString();
        }
        List<?> list = (List<?>) value;
        if (list.isEmpty()) return "[]";
        sb.append("[\n");
        for (int i = 0; i < list.size(); i++) {
            sb.append(inner).append(toJson(list.get(i), inner))
              .append(i + 1 < list.size() ? ",\n" : "\n");
        }
        return sb.append(indent).append(']').toString();
    }

    static String formatNumber(double v) {
        if (Double.isNaN(v) || Double.isInfinite(v)) return "null";
        if (v == Math.rint(v) && Math.abs(v) < 1e15) return Long.toString((long) v);
        return Double.toString(v);
    }
}

// Fintech Math Bootcamp · Lesson 039 of 120
// Histograms and Empirical Distribution Functions
// Module 04: Location, Ranking, and Exploratory Summaries
//
// Scenario: A histogram changes with bins; an ECDF preserves sample order
// Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
//
// Try it:   Where does 9 go with these half-open bins?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

import (
	"encoding/json"
	"fmt"
)

// Histogram holds half-open bin counts and one point of the empirical CDF.
type Histogram struct {
	Counts  []int   `json:"counts"`
	EcdfAt2 float64 `json:"ecdfAt2"`
}

func lesson039() Histogram {
	x := []float64{1, 2, 2, 4, 9}
	edges := []float64{0, 3, 6, 9, 12}
	// Half-open bins [lo, hi): a value on an edge goes to the bin that starts there.
	counts := make([]int, len(edges)-1)
	for i := range counts {
		for _, v := range x {
			if v >= edges[i] && v < edges[i+1] {
				counts[i]++
			}
		}
	}
	atOrBelow2 := 0
	for _, v := range x {
		if v <= 2 {
			atOrBelow2++
		}
	}
	return Histogram{Counts: counts, EcdfAt2: float64(atOrBelow2) / float64(len(x))}
}

func main() {
	out, _ := json.MarshalIndent(lesson039(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 039 of 120
 * Histograms and Empirical Distribution Functions
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A histogram changes with bins; an ECDF preserves sample order
 * Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
 *
 * Try it:   Where does 9 go with these half-open bins?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

#include <algorithm>
#include <charconv>
#include <cmath>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

struct Json {
    enum class Kind { Null, Number, Text, Array, Object };
    Kind kind = Kind::Null;
    double number = 0;
    std::string text;
    std::vector<std::string> keys;  // object keys, parallel to items
    std::vector<Json> items;        // array elements or object values
};

Json num(double v) { Json j; j.kind = Json::Kind::Number; j.number = v; return j; }
Json str(const std::string& s) { Json j; j.kind = Json::Kind::Text; j.text = s; return j; }
Json arr(const std::vector<Json>& values) { Json j; j.kind = Json::Kind::Array; j.items = values; return j; }

Json arr(const std::vector<double>& values) {
    std::vector<Json> items;
    for (double v : values) items.push_back(num(v));
    return arr(items);
}

Json obj(const std::vector<std::pair<std::string, Json>>& fields) {
    Json j;
    j.kind = Json::Kind::Object;
    for (const auto& [key, value] : fields) { j.keys.push_back(key); j.items.push_back(value); }
    return j;
}

std::string formatNumber(double v) {
    if (!std::isfinite(v)) return "null";
    char buf[64];
    auto end = std::to_chars(buf, buf + sizeof buf, v).ptr;  // shortest round-trip form
    return std::string(buf, end);
}

void writeJson(std::ostream& out, const Json& j, const std::string& indent) {
    switch (j.kind) {
    case Json::Kind::Null: out << "null"; return;
    case Json::Kind::Number: out << formatNumber(j.number); return;
    case Json::Kind::Text: out << '"' << j.text << '"'; return;
    default: break;
    }
    bool isObject = j.kind == Json::Kind::Object;
    if (j.items.empty()) { out << (isObject ? "{}" : "[]"); return; }
    std::string inner = indent + "  ";
    out << (isObject ? "{\n" : "[\n");
    for (size_t i = 0; i < j.items.size(); ++i) {
        out << inner;
        if (isObject) out << '"' << j.keys[i] << "\": ";
        writeJson(out, j.items[i], inner);
        out << (i + 1 < j.items.size() ? ",\n" : "\n");
    }
    out << indent << (isObject ? '}' : ']');
}

// --- Lesson ---

Json lesson039() {
    const std::vector<double> x = {1, 2, 2, 4, 9};
    const std::vector<double> edges = {0, 3, 6, 9, 12};
    // Half-open bins [lo, hi): a value on an edge goes to the bin that starts there.
    std::vector<double> counts;
    for (size_t i = 0; i + 1 < edges.size(); ++i) {
        double lo = edges[i], hi = edges[i + 1];
        counts.push_back(std::count_if(x.begin(), x.end(), [=](double v) { return v >= lo && v < hi; }));
    }
    double atOrBelow2 = std::count_if(x.begin(), x.end(), [](double v) { return v <= 2; });
    return obj({{"counts", arr(counts)}, {"ecdfAt2", num(atOrBelow2 / x.size())}});
}

int main() {
    writeJson(std::cout, lesson039(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 039 of 120
// Histograms and Empirical Distribution Functions
// Module 04: Location, Ranking, and Exploratory Summaries
//
// Scenario: A histogram changes with bins; an ECDF preserves sample order
// Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
//
// Try it:   Where does 9 go with these half-open bins?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

#[allow(dead_code)]
enum Json {
    Null,
    Num(f64),
    Str(String),
    Arr(Vec<Json>),
    Obj(Vec<(String, Json)>),
}

#[allow(dead_code)]
fn nums(values: &[f64]) -> Json {
    Json::Arr(values.iter().map(|&v| Json::Num(v)).collect())
}

#[allow(dead_code)]
fn obj(fields: Vec<(&str, Json)>) -> Json {
    Json::Obj(fields.into_iter().map(|(k, v)| (k.to_string(), v)).collect())
}

fn format_number(v: f64) -> String {
    if !v.is_finite() {
        return "null".to_string();
    }
    if v.fract() == 0.0 && v.abs() < 1e15 {
        return format!("{}", v as i64);
    }
    format!("{:?}", v) // shortest round-trip form
}

impl Json {
    fn render(&self, indent: &str) -> String {
        let inner = format!("{}  ", indent);
        match self {
            Json::Null => "null".to_string(),
            Json::Num(v) => format_number(*v),
            Json::Str(s) => format!("\"{}\"", s),
            Json::Arr(items) if items.is_empty() => "[]".to_string(),
            Json::Obj(fields) if fields.is_empty() => "{}".to_string(),
            Json::Arr(items) => {
                let lines: Vec<String> = items.iter().map(|v| format!("{}{}", inner, v.render(&inner))).collect();
                format!("[\n{}\n{}]", lines.join(",\n"), indent)
            }
            Json::Obj(fields) => {
                let lines: Vec<String> = fields
                    .iter()
                    .map(|(k, v)| format!("{}\"{}\": {}", inner, k, v.render(&inner)))
                    .collect();
                format!("{{\n{}\n{}}}", lines.join(",\n"), indent)
            }
        }
    }
}

// --- Lesson ---

fn lesson039() -> Json {
    let x: [f64; 5] = [1.0, 2.0, 2.0, 4.0, 9.0];
    let edges: [f64; 5] = [0.0, 3.0, 6.0, 9.0, 12.0];
    // Half-open bins [lo, hi): a value on an edge goes to the bin that starts there.
    let counts: Vec<f64> = edges
        .windows(2)
        .map(|bin| x.iter().filter(|&&v| v >= bin[0] && v < bin[1]).count() as f64)
        .collect();
    let ecdf_at_2 = x.iter().filter(|&&v| v <= 2.0).count() as f64 / x.len() as f64;
    obj(vec![("counts", nums(&counts)), ("ecdfAt2", Json::Num(ecdf_at_2))])
}

fn main() {
    println!("{}", lesson039().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 039 of 120
 * Histograms and Empirical Distribution Functions
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A histogram changes with bins; an ECDF preserves sample order
 * Rule:     Fₙ(x) = count(Xᵢ ≤ x)/n
 *
 * Try it:   Where does 9 go with these half-open bins?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

using System;
using System.Linq;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true };
Console.WriteLine(JsonSerializer.Serialize(Lesson039(), options));

static object Lesson039()
{
    double[] x = { 1, 2, 2, 4, 9 };
    double[] edges = { 0, 3, 6, 9, 12 };
    // Half-open bins [lo, hi): a value on an edge goes to the bin that starts there.
    int[] counts = edges.SkipLast(1)
        .Select((lo, i) => x.Count(v => v >= lo && v < edges[i + 1]))
        .ToArray();
    double ecdfAt2 = (double)x.Count(v => v <= 2) / x.Length;
    return new { counts, ecdfAt2 };
}