Bootstrap Confidence Interval

import random
import statistics
from collections.abc import Callable, Sequence


def bootstrap_confidence_interval(
    sample: Sequence[float],
    *,
    statistic: Callable[[Sequence[float]], float] = statistics.mean,
    iterations: int = 2000,
    confidence: float = 0.95,
    seed: int | None = None,
) -> tuple[float, float, float]:
    if not sample:
        raise ValueError("sample must not be empty")
    if not 0 < confidence < 1:
        raise ValueError("confidence must be between 0 and 1")
    if iterations < 100:
        raise ValueError("use at least 100 iterations")
    rng = random.Random(seed)
    size = len(sample)
    estimates: list[float] = []
    for _ in range(iterations):
        resample = [sample[rng.randrange(size)] for _ in range(size)]
        estimates.append(statistic(resample))
    estimates.sort()
    alpha = (1 - confidence) / 2
    lower = estimates[int(alpha * iterations)]
    upper = estimates[min(iterations - 1, int((1 - alpha) * iterations))]
    return lower, upper, statistic(sample)


def main() -> None:
    latencies = [12.0, 15.5, 11.2, 40.0, 13.8, 14.1, 16.0, 12.9, 55.0, 13.0]
    lower, upper, observed = bootstrap_confidence_interval(
        latencies, iterations=4000, seed=42
    )
    print(f"mean={observed:.2f} 95% CI=({lower:.2f}, {upper:.2f})")

    median_lower, median_upper, _ = bootstrap_confidence_interval(
        latencies,
        statistic=statistics.median,
        iterations=4000,
        seed=7,
    )
    print(f"median CI=({median_lower:.2f}, {median_upper:.2f})")


if __name__ == "__main__":
    main()