@railpath/finance-toolkit/dist/risk/calculateKurtosis.d.ts

Production-ready finance library for portfolio construction, risk analytics, quantitative metrics, and ML-based regime detection

/**
 * Calculate Kurtosis (Fourth Moment) of a dataset
 *
 * Kurtosis measures the "tailedness" of the distribution:
 * - Excess Kurtosis > 0: Heavy tails (leptokurtic) - more extreme values than normal distribution
 * - Excess Kurtosis < 0: Light tails (platykurtic) - fewer extreme values than normal distribution
 * - Excess Kurtosis = 0: Normal distribution (mesokurtic)
 *
 * This function returns the excess kurtosis (kurtosis - 3), which is commonly used in finance.
 *
 * Formula: Excess Kurtosis = E[(X - μ)⁴] / σ⁴ - 3
 * Where:
 * - μ = mean
 * - σ = standard deviation
 * - E[(X - μ)⁴] = fourth central moment
 * - The -3 makes excess kurtosis = 0 for normal distribution
 *
 * @param data Array of numbers to calculate kurtosis for
 * @returns Excess kurtosis value
 *
 * @example
 * ```typescript
 * const returns = [0.01, 0.02, -0.01, 0.03, -0.02, -0.05, 0.01];
 * const kurtosis = calculateKurtosis(returns);
 * console.log('Excess Kurtosis:', kurtosis); // 2.45 (fat tails)
 * ```
 */
export declare function calculateKurtosis(data: number[]): number;