Z-Score, Robust Z-Score, and Standardization

/**
 * Fintech Math Bootcamp · Lesson 048 of 120
 * Z-Score, Robust Z-Score, and Standardization
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Standardizing alerts without turning unusual into fraudulent
 * Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
 *
 * Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson048() {
  const observed = 9, mean = 3.6, sd = Math.sqrt(10.3);
  const median = 2, rawMAD: number = 1;
  const result = {z:(observed-mean)/sd,
    robustZ: rawMAD===0 ? null : .67448975*(observed-median)/rawMAD};
  return result;
}

export const checkedResult = {"z":1.6825777726943407,"robustZ":4.72142825};

// Run this file directly: npx tsx lessons/05-dispersion-shape-and-robust-statistics/048-z-score-robust-z-score-and-standardization.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson048(), null, 2));
}

# Fintech Math Bootcamp · Lesson 048 of 120
# Z-Score, Robust Z-Score, and Standardization
# Module 05: Dispersion, Shape, and Robust Statistics
#
# Scenario: Standardizing alerts without turning unusual into fraudulent
# Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
#
# Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json
import math


def lesson048() -> dict:
    observed, mean, sd = 9, 3.6, math.sqrt(10.3)
    median, raw_mad = 2, 1
    return {
        "z": (observed - mean) / sd,
        # A zero MAD has no robust scale, so the robust score is undefined (null).
        "robustZ": None if raw_mad == 0 else 0.67448975 * (observed - median) / raw_mad,
    }


if __name__ == "__main__":
    print(json.dumps(lesson048(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 048 of 120
 * Z-Score, Robust Z-Score, and Standardization
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Standardizing alerts without turning unusual into fraudulent
 * Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
 *
 * Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
 * 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> lesson048() {
        double observed = 9, mean = 3.6, sd = Math.sqrt(10.3);
        double median = 2, rawMAD = 1;
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("z", (observed - mean) / sd);
        // A zero MAD has no robust scale, so the robust score is undefined (null).
        result.put("robustZ", rawMAD == 0 ? null : (Double) (0.67448975 * (observed - median) / rawMAD));
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson048(), ""));
    }

    // --- 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 048 of 120
// Z-Score, Robust Z-Score, and Standardization
// Module 05: Dispersion, Shape, and Robust Statistics
//
// Scenario: Standardizing alerts without turning unusual into fraudulent
// Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
//
// Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

import (
	"encoding/json"
	"fmt"
	"math"
)

// Scores holds the classical z-score and the median/MAD robust z-score.
// RobustZ is a pointer so an undefined score prints as null.
type Scores struct {
	Z       float64  `json:"z"`
	RobustZ *float64 `json:"robustZ"`
}

func lesson048() Scores {
	observed, mean, sd := 9.0, 3.6, math.Sqrt(10.3)
	median, rawMAD := 2.0, 1.0
	result := Scores{Z: (observed - mean) / sd}
	if rawMAD != 0 {
		robustZ := 0.67448975 * (observed - median) / rawMAD
		result.RobustZ = &robustZ
	}
	return result
}

func main() {
	out, _ := json.MarshalIndent(lesson048(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 048 of 120
 * Z-Score, Robust Z-Score, and Standardization
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Standardizing alerts without turning unusual into fraudulent
 * Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
 *
 * Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <optional>
#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 lesson048() {
    const double observed = 9, mean = 3.6, sd = std::sqrt(10.3);
    const double median = 2, rawMAD = 1;
    // A zero MAD has no robust scale, so the robust score is undefined (null).
    std::optional<double> robustZ;
    if (rawMAD != 0) robustZ = 0.67448975 * (observed - median) / rawMAD;
    return obj({
        {"z", num((observed - mean) / sd)},
        {"robustZ", robustZ ? num(*robustZ) : Json{}},
    });
}

int main() {
    writeJson(std::cout, lesson048(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 048 of 120
// Z-Score, Robust Z-Score, and Standardization
// Module 05: Dispersion, Shape, and Robust Statistics
//
// Scenario: Standardizing alerts without turning unusual into fraudulent
// Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
//
// Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
// 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 lesson048() -> Json {
    let (observed, mean, sd) = (9.0, 3.6, 10.3_f64.sqrt());
    let (median, raw_mad): (f64, f64) = (2.0, 1.0);
    // A zero MAD has no robust scale, so the robust score is undefined (null).
    let robust_z = if raw_mad == 0.0 {
        Json::Null
    } else {
        Json::Num(0.67448975 * (observed - median) / raw_mad)
    };
    obj(vec![("z", Json::Num((observed - mean) / sd)), ("robustZ", robust_z)])
}

fn main() {
    println!("{}", lesson048().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 048 of 120
 * Z-Score, Robust Z-Score, and Standardization
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Standardizing alerts without turning unusual into fraudulent
 * Rule:     z = (x−mean)/s; robust z = 0.67448975(x−median)/MAD
 *
 * Try it:   Does a robust z-score of 4.72 prove the transaction is fraudulent?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/z-score-robust-z-score-and-standardization/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

using System;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true };
Console.WriteLine(JsonSerializer.Serialize(Lesson048(), options));

static object Lesson048()
{
    double observed = 9, mean = 3.6, sd = Math.Sqrt(10.3);
    double median = 2, rawMad = 1;
    // A zero MAD has no robust scale, so the robust score is undefined (null).
    double? robustZ = rawMad == 0 ? null : 0.67448975 * (observed - median) / rawMad;
    return new { z = (observed - mean) / sd, robustZ };
}