htest-tools 0.2.6

Simple Z-test helper functions (one mean and two proportions)

🧪 htest-tools

A complete statistics hub for Hypothesis Testing, UMP Tests, Estimator Properties, and MLE.

htest-tools is a Python library designed to streamline statistical analysis. It provides clean results, automatic interpretations, and robust data structures for Z-tests, Neyman-Pearson (MP/UMP) tests, Cramer-Rao Lower Bound (CRLB) calculations, and Maximum Likelihood Estimation (MLE).

Here is a comprehensive, formatted README.md file ready for PyPI, organized based on the documentation you provided.

# 🧪 htest-tools

**A complete statistics hub for Hypothesis Testing, UMP Tests, Estimator Properties, and MLE.**

`htest-tools` is a Python library designed to streamline statistical analysis. It provides clean results, automatic interpretations, and robust data structures for Z-tests, Neyman-Pearson (MP/UMP) tests, Cramer-Rao Lower Bound (CRLB) calculations, and Maximum Likelihood Estimation (MLE).

---

## 📦 Installation

```bash
pip install htest-tools

---

🚀 Features

• Z-Tests & Confidence Intervals: Standard tests for means and proportions with automatic interpretations.
• Neyman–Pearson / UMP Tests: Implements Most Powerful and Uniformly Most Powerful tests for Binomial, Poisson, and Normal distributions.
• Estimator Analysis: Calculates bias, variance, efficiency, and CRLB.
• Maximum Likelihood Estimation: Computes MLEs with handling for edge cases/degenerate data.
• Structured Outputs: All functions return clear, typed dataclasses (e.g., TestResult, EstimatorSummary, MLEOutput) containing full context, p-values, and logical interpretations.

---

📝 Usage Example

from htest_tools import (
    np_binom, np_norm, np_pois,
    est_norm_mean, est_binom_p,
    mle_exp
)
import numpy as np

# 1. Neyman–Pearson Test (Binomial)
# Testing H0: p=0.4 vs H1: p=0.6 with 12 successes in 20 trials
result = np_binom(x=12, n=20, p0=0.4, p1=0.6, alternative="greater")
print(f"Reject Null: {result.reject_h0}")
print(f"Interpretation: {result.interpretation}")

# 2. Estimator Properties
# Analyze sample mean properties for Normal distribution
sample = np.random.normal(10, 2, 50)
est_summary = est_norm_mean(sample, sigma2_known=4)
print(f"Efficiency: {est_summary.efficient}")
print(f"CRLB: {est_summary.crlb}")

# 3. Maximum Likelihood Estimation
# Estimate lambda for Exponential distribution
exp_data = np.random.exponential(scale=2, size=100)
mle_result = mle_exp(exp_data)
print(f"Estimated Lambda: {mle_result.parameters_hat}")

---

📚 API Reference

Z-Tests & Confidence Intervals (htests.py)

Standard hypothesis tests and confidence intervals.

Hypothesis Tests

Function	Description	Parameters
z_test_one_mean	Z-test for one population mean	xbar, mu0, sigma, n, alpha, alternative
z_test_two_proportions	Z-test comparing two proportions	x1, n1, x2, n2, alpha, alternative

Confidence Intervals

Function	Description	Parameters
ci_one_mean_t	CI for mean (σ unknown)	xbar, s, n, alpha
ci_one_mean_z	CI for mean (σ known)	xbar, sigma, n, alpha
ci_two_means_independent_t	CI for diff in means (t-test)	xbar1, s1, n1, xbar2, s2, n2, alpha
ci_two_means_independent_z	CI for diff in means (z-test)	xbar1, sigma1, n1, xbar2, sigma2, n2, alpha

---

Neyman–Pearson / UMP Tests (np_lemma_tests.py)

Implements MP/UMP tests. Returns a TestResult object containing the statistic, critical region, p-value, and rejection logic.

Return Object: TestResult

Functions

• np_binom(x, n, p0, p1, alpha, alternative)

  • Distribution: Binomial(n, p)
  • Purpose: MP/UMP test for proportion $p$.
  • Hypotheses: $H_0: p = p_0$ vs $H_1: p = p_1$.

• np_pois(x, lambda0, lambda1, alpha, alternative)

  • Distribution: Poisson(λ)
  • Purpose: MP/UMP test for rate $\lambda$.

• np_norm(xbar, n, mu0, mu1, sigma, alpha, alternative)

  • Distribution: Normal(μ, σ known)
  • Purpose: MP/UMP z-test for mean $\mu$.

---

Estimator Properties & CRLB (estimator_properties.py)

Analyzes the properties of an estimator, including Bias, Variance, and Efficiency compared to the Cramer-Rao Lower Bound (CRLB).

Return Object: EstimatorSummary

Estimator Analyzers

Function	Distribution	Computes
est_norm_mean(sample, sigma2_known)	Normal	Bias, Var, Efficiency of $\bar{X}$
est_binom_p(k, n, p_true)	Binomial	Properties of $\hat{p} = k/n$
est_pois_lam(counts, lambda_true)	Poisson	Properties of $\hat{\lambda} = \bar{X}$

CRLB Utilities

Calculates the theoretical lower bound for variance.

• crlb_norm(sigma2, n): CRLB for $\mu$
• crlb_binom(p, n): CRLB for $p$
• crlb_pois(lam, n): CRLB for $\lambda$

---

Maximum Likelihood Estimation (mle_est.py)

Computes MLE parameters for common distributions, handling boundary conditions and degenerate cases.

Return Object: MLEOutput

Functions

• mle_norm(sample)

  • Returns: $\hat{\mu}$ (mean), $\hat{\sigma}^2$ (variance with denominator $n$).
  • Note: Handles degenerate cases where all values are equal.

• mle_binom(k, n)

  • Returns: $\hat{p} = k/n$.
  • Note: Handles boundary cases ($k=0 \to \hat{p}=0$, $k=n \to \hat{p}=1$).

• mle_exp(sample)

  • Returns: $\hat{\lambda} = 1 / \bar{X}$.
  • Note: If all data is 0, returns $\hat{\lambda} = \infty$.

---

🔗 Public API

The following functions are exposed via __all__:

• z_test_one_mean, z_test_two_proportions
• ci_one_mean_t, ci_one_mean_z
• ci_two_means_independent_t, ci_two_means_independent_z
• np_binom, np_pois, np_norm
• est_norm_mean, est_binom_p, est_pois_lam
• crlb_norm, crlb_binom, crlb_pois
• mle_norm, mle_binom, mle_exp

---

📄 License

MIT