114 lines
3.3 KiB
Python
114 lines
3.3 KiB
Python
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"""统计推断：区间估计、假设检验、分布拟合。
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原建议里的 `mean_test`/`proportion_test`/`distribution_pdf`/`distribution_cdf`/
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`distribution_ppf`/`sample_distribution` 都是 scipy 的一行转发，已删。
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需要 pdf/cdf/ppf 时，用 `fit_distribution(...).dist.pdf(...)` 即可。
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"""
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from __future__ import annotations
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from typing import Any
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__all__ = [
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"anova",
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"chi_square_test",
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"confidence_interval",
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"correlation_matrix",
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"fit_distribution",
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"goodness_of_fit",
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"t_test",
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]
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def correlation_matrix(data: Any, method: str = "pearson", min_periods: int = 1) -> Any:
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"""相关矩阵 + 显著性星标。
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Returns
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-------
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DataFrame，值 = 相关系数；`min_periods` 控制缺失值容差。
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Examples
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--------
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>>> correlation_matrix(df).round(3) # doctest: +SKIP
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"""
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# TODO(L0)
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raise NotImplementedError
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def confidence_interval(
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x: Any,
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confidence: float = 0.95,
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method: str = "normal",
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) -> tuple[float, float]:
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"""均值或比例的置信区间。
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Parameters
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----------
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method:
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`"normal"`：`mean ± z·s/√n`（n 大时用）；
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`"t"`：小样本用 t 分布（更保守，n < 30 建议用这个）；
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`"proportion"`：比例的标准误 `√(p(1-p)/n)`。
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Examples
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--------
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>>> lo, hi = confidence_interval([1, 2, 3, 4, 5], confidence=0.95)
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"""
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# TODO(L0)
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raise NotImplementedError
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def t_test(a: Any, b: Any | None = None, value: float = 0.0, equal_var: bool = False, paired: bool = False, alpha: float = 0.05) -> Any:
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"""t 检验。`b=None` 时是单样本检验。
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Returns
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-------
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dict：`{"statistic", "pvalue", "df", "significant", "conclusion"}`。
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`conclusion` 是一句能直接抄进论文的中文结论。
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"""
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# TODO(L1)
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raise NotImplementedError
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def anova(*groups: Any, alpha: float = 0.05) -> Any:
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"""单因素方差分析：多组均值是否相同。
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Returns
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-------
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dict：`{"F", "pvalue", "conclusion"}`。
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"""
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# TODO(L1)
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raise NotImplementedError
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def chi_square_test(observed: Any, expected: Any | None = None, alpha: float = 0.05) -> Any:
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"""卡方检验：观察频数与期望频数是否一致（分类变量的独立性 / 拟合优度）。"""
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# TODO(L1)
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raise NotImplementedError
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def fit_distribution(x: Any, candidates: tuple[str, ...] = ("norm", "lognorm", "gamma", "expon", "uniform")) -> Any:
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"""对候选分布逐个拟合，按 AIC（或 KS 统计量）排序。
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Returns
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-------
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`Result`：`data` 是排好序的候选表；`params["best"]` 是最优分布名，
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`extras["dist"]` 是可直接调 `.pdf / .cdf / .ppf / `.rvs` 的 scipy 分布对象。
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Notes
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-----
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这是"反正态题"的标准做法：先看图 → 候选分布拟合 → 比较 AIC → 做 KS 检验。
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Examples
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--------
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>>> r = fit_distribution(data) # doctest: +SKIP
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>>> r.params["best"] # doctest: +SKIP
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'lognorm'
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"""
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# TODO(L1)
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raise NotImplementedError
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def goodness_of_fit(x: Any, dist: str = "norm", method: str = "ks") -> Any:
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"""拟合优度检验：`"ks"`（连续）/ `"chi2"`（分箱）。"""
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# TODO(L1)
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raise NotImplementedError
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