import math import numpy as np import pandas as pd from statistics import NormalDist def _validate_conf_level(conf_level): if conf_level is None: raise ValueError("Confidence level must be provided.") cl = float(conf_level) if cl >= 1.0: cl = cl / 100.0 if not (0.0 < cl < 1.0): raise ValueError("Confidence level must be between 0 and 1 (exclusive).") return cl def _z_critical(conf_level): cl = _validate_conf_level(conf_level) alpha = 1.0 - cl return NormalDist().inv_cdf(1.0 - alpha / 2.0) def _t_critical(conf_level, df): if df is None or df <= 0: raise ValueError("Degrees of freedom must be positive for t critical.") cl = _validate_conf_level(conf_level) alpha = 1.0 - cl p = 1.0 - alpha / 2.0 z = NormalDist().inv_cdf(p) nu = float(df) z2 = z * z z3 = z2 * z z5 = z3 * z2 z7 = z5 * z2 t_approx = ( z + (z3 + z) / (4.0 * nu) + (5.0 * z5 + 16.0 * z3 + 3.0 * z) / (96.0 * nu * nu) + (3.0 * z7 + 19.0 * z5 + 17.0 * z3 - 15.0 * z) / (384.0 * nu * nu * nu) ) return t_approx def _se_mean_from_sigma(sigma, n): if n is None or n <= 0: raise ValueError("Sample size n must be positive.") if sigma is None or sigma < 0: raise ValueError("Standard deviation must be non-negative.") return float(sigma) / math.sqrt(n) def _se_proportion_wald(p_hat, n): if n is None or n <= 0: raise ValueError("n must be positive.") return math.sqrt(max(p_hat * (1.0 - p_hat), 0.0) / n) def ci_mean_z(xbar, sigma, n, conf_level=0.95): z = _z_critical(conf_level) se = _se_mean_from_sigma(sigma, n) me = z * se lower = xbar - me upper = xbar + me return { "method": "Z", "mean": float(xbar), "n": int(n), "sigma": float(sigma), "se": se, "critical_value": z, "margin_of_error": me, "lower": lower, "upper": upper, "conf_level": _validate_conf_level(conf_level), } def ci_mean_t(xbar, s, n, conf_level=0.95): df = int(n) - 1 if df < 1: raise ValueError("For t-based CI you need at least n >= 2 (df >= 1).") tcrit = _t_critical(conf_level, df) se = _se_mean_from_sigma(s, n) me = tcrit * se lower = xbar - me upper = xbar + me return { "method": "T", "mean": float(xbar), "n": int(n), "s": float(s), "df": df, "se": se, "critical_value": tcrit, "margin_of_error": me, "lower": lower, "upper": upper, "conf_level": _validate_conf_level(conf_level), } def ci_proportion_wald(x=None, n=None, p_hat=None, conf_level=0.95): if p_hat is None: if x is None or n is None: raise ValueError("Provide either (x, n) or p_hat.") if n <= 0 or x < 0 or x > n: raise ValueError("Require 0 <= x <= n and n > 0.") p_hat = x / n cl = _validate_conf_level(conf_level) z = _z_critical(cl) se = _se_proportion_wald(p_hat, n if n is not None else 1e-12) me = z * se lower = max(0.0, p_hat - me) upper = min(1.0, p_hat + me) return { "method": "Wald", "p_hat": float(p_hat), "n": int(n) if n is not None else None, "critical_value": z, "se": se, "margin_of_error": me, "lower": lower, "upper": upper, "conf_level": cl, } def ci_proportion_wilson(x=None, n=None, p_hat=None, conf_level=0.95): if p_hat is None: if x is None or n is None: raise ValueError("Provide either (x, n) or p_hat.") if n <= 0 or x < 0 or x > n: raise ValueError("Require 0 <= x <= n and n > 0.") p_hat = x / n cl = _validate_conf_level(conf_level) z = _z_critical(cl) if n is None or n <= 0: raise ValueError("n must be positive for Wilson interval.") denom = 1.0 + (z * z) / n center = (p_hat + (z * z) / (2.0 * n)) / denom rad = (z * math.sqrt((p_hat * (1.0 - p_hat) + (z * z) / (4.0 * n)) / n)) / denom lower = max(0.0, center - rad) upper = min(1.0, center + rad) return { "method": "Wilson", "p_hat": float(p_hat), "n": int(n), "critical_value": z, "center": center, "radius": rad, "lower": lower, "upper": upper, "conf_level": cl, } def parse_numeric_list(s): if not s or not isinstance(s, str): return [] raw = s.replace(",", " ").replace(";", " ").split() vals = [] for token in raw: try: vals.append(float(token)) except ValueError: continue return vals def sample_mean_and_sd(data): n = len(data) if n == 0: raise ValueError("No data provided.") xbar = sum(data) / n if n < 2: return xbar, 0.0, n var = sum((x - xbar) ** 2 for x in data) / (n - 1) s = math.sqrt(var) return xbar, s, n