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| import numpy as np
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| from scipy.stats import norm
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|
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| from .estimators import estimate_sigma
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| def pi_median(
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| *,
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| data,
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| alpha,
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| sigma_estimator,
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| ):
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| """
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| Asymptotic prediction interval based on the sample median.
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| scale = sqrt(σ² + πσ² / (2n)) = σ * sqrt(1 + π/(2n))
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| σ is computed with the user-chosen deviation estimator.
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| """
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| data = np.asarray(data)
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| n = len(data)
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| median_hat = np.median(data)
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|
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| sigma_hat = estimate_sigma(
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| data=data,
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| estimator=sigma_estimator,
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| )
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| scale = np.sqrt(sigma_hat**2 + np.pi * sigma_hat**2 / (2 * n))
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| return (
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| norm.ppf(alpha / 2, median_hat, scale),
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| norm.ppf(1 - alpha / 2, median_hat, scale),
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| )
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|
