Generates N values in a standard distribution summing to X

generate_standard_distribution.ts

/**
 * Generates a normally distributed random number with an absolute value.
 * @returns A positive random number following a standard normal distribution.
 */
function boxMullerRandomPositive(): number {
  let u = 0, v = 0;
  while (u === 0) u = Math.random();
  while (v === 0) v = Math.random();
  return Math.abs(Math.sqrt(-2.0 * Math.log(u)) * Math.cos(2.0 * Math.PI * v));
}

/**
 * Generates an array of N positive values in a standard distribution that sum to X.
 * @param N - The number of values to generate.
 * @param X - The target sum for the generated values.
 * @returns An array of N positive numbers in a standard distribution that sum to X.
 */
function generatePositiveStandardDistribution(N: number, X: number): number[] {
  let generatedValues: number[] = new Array(N).fill(0).map(() => boxMullerRandomPositive());
  
  // Calculate the current sum of generated values
  const currentSum = generatedValues.reduce((acc, val) => acc + val, 0);
  
  // Scale the values so that their sum becomes X
  const scalingFactor = X / currentSum;
  generatedValues = generatedValues.map(val => val * scalingFactor);
  
  return generatedValues;
}

// Example usage
const N = 100;
const X = 10;
const result = generatePositiveStandardDistribution(N, X);
console.log(`Generated positive values: ${result}`);
console.log(`Sum: ${result.reduce((acc, val) => acc + val, 0)}`);