# Author: Nikolaos Perrakis <nikos@nannyml.com>
#
# License: Apache Software License 2.0
from logging import getLogger
from typing import Tuple
import numpy as np
import pandas as pd
from scipy.stats import gaussian_kde, moment
logger = getLogger(__name__)
[docs]def summary_stats_std_sampling_error_components(col: pd.Series) -> Tuple:
"""
Calculate sampling error components for Summary Stats Standard Deviation
using reference data.
Parameters
----------
col: pd.Series
column for which we are calculating sampling error components
Returns
-------
(std, moment_4th): Tuple[np.ndarray]
"""
std = col.std()
moment_4th = moment(col.to_numpy(), 4)
return (std, moment_4th)
[docs]def summary_stats_std_sampling_error(sampling_error_components, col) -> float:
"""
Calculate sampling error for Summary Stats Standard Deviation
using reference data.
Standard Error of Standard Deviation, https://stats.stackexchange.com/a/157305
CR Rao (1973) Linear Statistical Inference and its Applications 2nd Ed, John Wiley & Sons, NY
Parameters
----------
sampling_error_components:
a set of parameters that were derived from reference data.
col:
the (analysis) column you want to calculate sampling error for.
Returns
-------
sampling_error: float
"""
_std = sampling_error_components[0]
_mu4 = sampling_error_components[1]
_size = col.shape[0]
err_var_parenthesis_part = _mu4 - ((_size - 3) * (_std**4) / (_size - 1))
if not (np.isfinite(err_var_parenthesis_part) and err_var_parenthesis_part >= 0):
logger.debug(
"Summary Stats sampling error calculation imputed to nan because of non finite positive parenthesis factor."
)
return np.nan
err_var = np.sqrt((1 / _size) * err_var_parenthesis_part)
return (1 / (2 * _std)) * err_var