/**
 * Statistical analysis utilities.
 * Pure functions with zero dependencies - can be used standalone for any data analysis.
 *
 * @module
 */
/**
 * Calculate the mean (average) of an array of numbers.
 */
export declare const stats_mean: (values: Array<number>) => number;
/**
 * Calculate the median of an array of numbers.
 * NaN values are filtered out before computing.
 */
export declare const stats_median: (values: Array<number>) => number;
/**
 * Calculate the standard deviation of an array of numbers.
 * Uses population standard deviation (divides by n, not n-1).
 * For benchmarks with many samples, this is typically appropriate.
 */
export declare const stats_std_dev: (values: Array<number>, mean?: number) => number;
/**
 * Calculate the variance of an array of numbers.
 */
export declare const stats_variance: (values: Array<number>, mean?: number) => number;
/**
 * Calculate a percentile of an array of numbers using linear interpolation.
 * Uses the "R-7" method (default in R, NumPy, Excel) which interpolates between
 * data points for more accurate percentile estimates, especially with smaller samples.
 * @param p - percentile (0-1, e.g., 0.95 for 95th percentile)
 */
export declare const stats_percentile: (values: Array<number>, p: number) => number;
/**
 * Calculate the coefficient of variation (CV).
 * CV = standard deviation / mean, expressed as a ratio.
 * Useful for comparing relative variability between datasets.
 */
export declare const stats_cv: (mean: number, std_dev: number) => number;
/**
 * Calculate min and max values.
 * NaN values are ignored.
 */
export declare const stats_min_max: (values: Array<number>) => {
    min: number;
    max: number;
};
/**
 * Result from outlier detection.
 */
export interface StatsOutlierResult {
    /** Values after removing outliers */
    cleaned: Array<number>;
    /** Detected outlier values */
    outliers: Array<number>;
}
/**
 * Configuration options for IQR outlier detection.
 */
export interface StatsOutliersIqrOptions {
    /** Multiplier for IQR bounds (default: 1.5) */
    iqr_multiplier?: number;
    /** Minimum sample size to perform outlier detection (default: 3) */
    min_sample_size?: number;
}
/**
 * Detect outliers using the IQR (Interquartile Range) method.
 * Values outside [Q1 - multiplier*IQR, Q3 + multiplier*IQR] are considered outliers.
 */
export declare const stats_outliers_iqr: (values: Array<number>, options?: StatsOutliersIqrOptions) => StatsOutlierResult;
/**
 * Configuration options for MAD outlier detection.
 */
export interface StatsOutliersMadOptions {
    /** Modified Z-score threshold for outlier detection (default: 3.5) */
    z_score_threshold?: number;
    /** Extreme Z-score threshold when too many outliers detected (default: 5.0) */
    z_score_extreme?: number;
    /** MAD constant for normal distribution (default: 0.6745) */
    mad_constant?: number;
    /** Ratio threshold to switch to extreme mode (default: 0.3) */
    outlier_ratio_high?: number;
    /** Ratio threshold to switch to keep-closest mode (default: 0.4) */
    outlier_ratio_extreme?: number;
    /** Ratio of values to keep in keep-closest mode (default: 0.8) */
    outlier_keep_ratio?: number;
    /** Minimum sample size to perform outlier detection (default: 3) */
    min_sample_size?: number;
    /** Options to pass to IQR fallback when MAD is zero */
    iqr_options?: StatsOutliersIqrOptions;
}
/**
 * Detect outliers using the MAD (Median Absolute Deviation) method.
 * More robust than IQR for skewed distributions.
 * Uses modified Z-score: |0.6745 * (x - median) / MAD|
 * Values with modified Z-score > threshold are considered outliers.
 */
export declare const stats_outliers_mad: (values: Array<number>, options?: StatsOutliersMadOptions) => StatsOutlierResult;
/**
 * Common z-scores for confidence intervals.
 */
export declare const STATS_CONFIDENCE_Z_SCORES: Record<number, number>;
/**
 * Convert a confidence level (0-1) to a z-score.
 * Uses a lookup table for common values, approximates others.
 *
 * @throws Error if `level` is not in the open interval (0, 1)
 *
 * @example
 * ```ts
 * stats_confidence_level_to_z_score(0.95); // 1.96
 * stats_confidence_level_to_z_score(0.99); // 2.576
 * ```
 */
export declare const stats_confidence_level_to_z_score: (level: number) => number;
/**
 * Configuration options for confidence interval calculation.
 */
export interface StatsConfidenceIntervalOptions {
    /** Z-score for confidence level (default: 1.96 for 95% CI) */
    z_score?: number;
    /** Confidence level (0-1), alternative to z_score. If both provided, z_score takes precedence. */
    confidence_level?: number;
}
/**
 * Calculate confidence interval for the mean.
 * @returns `[lower_bound, upper_bound]`
 */
export declare const stats_confidence_interval: (values: Array<number>, options?: StatsConfidenceIntervalOptions) => [number, number];
/**
 * Calculate confidence interval from summary statistics (mean, std_dev, sample_size).
 * Useful when raw data is not available.
 * @returns `[lower_bound, upper_bound]`
 */
export declare const stats_confidence_interval_from_summary: (mean: number, std_dev: number, sample_size: number, options?: StatsConfidenceIntervalOptions) => [number, number];
/**
 * Result from Welch's t-test calculation.
 */
export interface StatsWelchTTestResult {
    /** The t-statistic */
    t_statistic: number;
    /** Welch-Satterthwaite degrees of freedom */
    degrees_of_freedom: number;
}
/**
 * Calculate Welch's t-test statistic and degrees of freedom.
 * Welch's t-test is more robust than Student's t-test when variances are unequal.
 *
 * Params suffixed `1` describe the first sample, `2` the second.
 */
export declare const stats_welch_t_test: (mean1: number, std1: number, n1: number, mean2: number, std2: number, n2: number) => StatsWelchTTestResult;
/**
 * Standard normal CDF approximation (Abramowitz and Stegun formula 7.1.26).
 */
export declare const stats_normal_cdf: (x: number) => number;
/**
 * Log gamma function approximation (Lanczos approximation).
 */
export declare const stats_ln_gamma: (z: number) => number;
/**
 * Approximate regularized incomplete beta function for p-value calculation.
 * Uses continued fraction expansion for reasonable accuracy.
 */
export declare const stats_incomplete_beta: (x: number, a: number, b: number) => number;
/**
 * Approximate two-tailed p-value from t-distribution.
 * For large df (>100), uses normal approximation.
 * For smaller df, uses incomplete beta function.
 *
 * @param t - absolute value of t-statistic
 * @param df - degrees of freedom
 * @returns two-tailed p-value
 */
export declare const stats_t_distribution_p_value: (t: number, df: number) => number;
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