"""
normality_checks.py

Module for normality check heuristics.
"""

from typing import Tuple


def iqr_tail_heaviness(iqr: float, sd: float) -> float:
    """Return ratio R = IQR/SD for tail heaviness checking."""
    return iqr / sd if sd != 0 else float("nan")


def quartile_z_scores(
    mean: float,
    sd: float,
    q1: float,
    q3: float,
) -> Tuple[float, float]:
    """Return observed z-scores for Q1 and Q3."""
    if sd == 0:
        return (float("nan"), float("nan"))
    q1_z = (q1 - mean) / sd
    q3_z = (q3 - mean) / sd
    return q1_z, q3_z


def pearson_skewness(mean: float, median: float, sd: float) -> float:
    """Return Pearson's moment coefficient of skewness."""
    return 3 * (mean - median) / sd if sd != 0 else float("nan")