Dr. QuantMaster MCP Server

// Mathematical helper functions /** * Error function (erf) approximation * Based on Abramowitz and Stegun formula 7.1.26 */ export function erf(x: number): number { // Constants const a1 = 0.254829592; const a2 = -0.284496736; const a3 = 1.421413741; const a4 = -1.453152027; const a5 = 1.061405429; const p = 0.3275911; // Save the sign of x const sign = x < 0 ? -1 : 1; x = Math.abs(x); // Approximation const t = 1.0 / (1.0 + p * x); const y = 1.0 - ((((a5 * t + a4) * t + a3) * t + a2) * t + a1) * t * Math.exp(-x * x); return sign * y; } /** * Standard normal CDF (cumulative distribution function) */ export function normalCDF(x: number): number { return 0.5 * (1 + erf(x / Math.sqrt(2))); } /** * Inverse error function approximation */ export function erfInv(x: number): number { const a = 0.147; const sign = x < 0 ? -1 : 1; x = Math.abs(x); const ln = Math.log(1 - x * x); const t1 = 2 / (Math.PI * a) + ln / 2; const t2 = ln / a; return sign * Math.sqrt(Math.sqrt(t1 * t1 - t2) - t1); } /** * Inverse standard normal CDF (quantile function) */ export function normalQuantile(p: number): number { return Math.sqrt(2) * erfInv(2 * p - 1); } /** * Power calculation for two-sample t-test */ export function calculatePower( n: number, effectSize: number, alpha: number = 0.05 ): number { const zAlpha = normalQuantile(1 - alpha / 2); const ncp = effectSize * Math.sqrt(n / 2); const power = 1 - normalCDF(zAlpha - ncp); return Math.min(Math.max(power, 0), 1); } /** * Sample size calculation for two-sample t-test */ export function calculateSampleSize( effectSize: number, alpha: number = 0.05, power: number = 0.80 ): number { const zAlpha = normalQuantile(1 - alpha / 2); const zBeta = normalQuantile(power); const n = 2 * Math.pow((zAlpha + zBeta) / effectSize, 2); return Math.ceil(n); }