1313"""
1414
1515__all__ = [
16- "resample" ,
1716 "bootstrap" ,
18- "variance" ,
19- "covariance" ,
2017 "confidence_interval" ,
18+ "covariance" ,
19+ "resample" ,
20+ "variance" ,
2121]
2222
23+ from collections .abc import Callable , Collection , Generator
2324from typing import (
2425 Any ,
25- Callable ,
26- Collection ,
27- Dict ,
28- Generator ,
29- List ,
3026 Optional ,
31- Tuple ,
32- Union ,
3327)
3428
3529import numpy as np
@@ -47,7 +41,7 @@ def resample(
4741 size : int = 100 ,
4842 method : str = "balanced" ,
4943 strata : Optional ["ArrayLike" ] = None ,
50- random_state : Optional [ Union [ np .random .Generator , int ]] = None ,
44+ random_state : np .random .Generator | int | None = None ,
5145) -> Generator [np .ndarray , None , None ]:
5246 """
5347 Return generator of bootstrap samples.
@@ -147,7 +141,7 @@ def resample(
147141 """
148142 sample_np = np .atleast_1d (sample )
149143 n_sample = len (sample_np )
150- args_np : List [np .ndarray ] = []
144+ args_np : list [np .ndarray ] = []
151145
152146 if args :
153147 if not isinstance (args [0 ], Collection ):
@@ -158,7 +152,7 @@ def resample(
158152 "deprecated" ,
159153 FutureWarning ,
160154 )
161- kwargs : Dict [str , Any ] = {
155+ kwargs : dict [str , Any ] = {
162156 "size" : size ,
163157 "method" : method ,
164158 "strata" : strata ,
@@ -381,7 +375,7 @@ def confidence_interval(
381375 cl : float = 0.95 ,
382376 ci_method : str = "bca" ,
383377 ** kwargs : Any ,
384- ) -> Tuple [float , float ]:
378+ ) -> tuple [float , float ]:
385379 """
386380 Calculate bootstrap confidence intervals.
387381
@@ -491,7 +485,7 @@ def _resample_ordinary_1(
491485
492486
493487def _resample_ordinary_n (
494- samples : List [np .ndarray ], size : int , rng : np .random .Generator
488+ samples : list [np .ndarray ], size : int , rng : np .random .Generator
495489) -> Generator [np .ndarray , None , None ]:
496490 n = len (samples [0 ])
497491 indices = np .arange (n )
@@ -513,7 +507,7 @@ def _resample_balanced_1(
513507
514508
515509def _resample_balanced_n (
516- samples : List [np .ndarray ], size : int , rng : np .random .Generator
510+ samples : list [np .ndarray ], size : int , rng : np .random .Generator
517511) -> Generator [np .ndarray , None , None ]:
518512 n = len (samples [0 ])
519513 indices = rng .permutation (n * size )
@@ -533,7 +527,7 @@ def _resample_extended_1(
533527
534528
535529def _resample_extended_n (
536- samples : List [np .ndarray ], size : int , rng : np .random .Generator
530+ samples : list [np .ndarray ], size : int , rng : np .random .Generator
537531) -> Generator [np .ndarray , None , None ]:
538532 n = len (samples [0 ])
539533 for i in range (size ):
@@ -543,7 +537,7 @@ def _resample_extended_n(
543537
544538def _fit_parametric_family (
545539 dist : stats .rv_continuous , sample : np .ndarray
546- ) -> Tuple [float , ...]:
540+ ) -> tuple [float , ...]:
547541 if dist == stats .multivariate_normal :
548542 # has no fit method...
549543 return np .mean (sample , axis = 0 ), np .cov (sample .T , ddof = 1 )
@@ -579,14 +573,14 @@ def _resample_parametric(
579573
580574def _confidence_interval_percentile (
581575 thetas : np .ndarray , alpha_half : float
582- ) -> Tuple [float , float ]:
576+ ) -> tuple [float , float ]:
583577 quant = quantile_function_gen (thetas )
584578 return quant (alpha_half ), quant (1 - alpha_half )
585579
586580
587581def _confidence_interval_bca (
588582 theta : float , thetas : np .ndarray , j_thetas : np .ndarray , alpha_half : float
589- ) -> Tuple [float , float ]:
583+ ) -> tuple [float , float ]:
590584 norm = stats .norm
591585
592586 # bias correction; implementation notes:
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