# FastBootstrap
<div align="center">
**⚡ Fast Python implementation of statistical bootstrap methods**
[](https://badge.fury.io/py/fastbootstrap)
[](https://www.python.org/downloads/release/python-3120/)
[](https://opensource.org/licenses/MIT)
[](https://github.com/psf/black)
*High-performance statistical bootstrap with parallel processing and comprehensive method support*
[Installation](#installation) • [Quick Start](#quick-start) • [Examples](#examples) • [Performance](#performance) • [API](#api-reference)
</div>
---
## 🚀 Features
- **Multiple Bootstrap Methods**: Percentile, BCa, Basic, Studentized, Spotify-style, and Poisson bootstrap
- **High Performance**: Parallel processing with joblib, optimized NumPy operations
- **Comprehensive Statistics**: Confidence intervals, p-values, effect sizes, power analysis, quantile-quantile analysis
- **Flexible API**: Unified interface with method auto-selection
- **Rich Visualizations**: Built-in plotting with matplotlib and plotly
- **Production Ready**: Extensive error handling, type hints
## 📦 Installation
```bash
pip install fastbootstrap
```
### 🛠️ Development Setup
```bash
git clone https://github.com/timofeytkachenko/fastbootstrap.git
cd fastbootstrap
pip install -e ".[dev]"
pre-commit install
```
## 🎯 Quick Start
```python
import numpy as np
import fastbootstrap as fb
# Generate sample data
np.random.seed(42)
control = np.random.normal(100, 15, 1000) # Control group
treatment = np.random.normal(105, 15, 1000) # Treatment group (+5% effect)
# Two-sample bootstrap test
result = fb.two_sample_bootstrap(control, treatment, plot=True)
print(f"P-value: {result['p_value']:.4f}")
print(f"Effect size: {result['statistic_value']:.2f}")
print(f"95% CI: [{result['confidence_interval'][0]:.2f}, {result['confidence_interval'][1]:.2f}]")
```
## 📊 Examples
### One-Sample Bootstrap
Estimate confidence intervals for a single sample statistic:
```python
import fastbootstrap as fb
import numpy as np
# Sample data
sample = np.random.exponential(2, 500)
# Basic percentile bootstrap
result = fb.one_sample_bootstrap(
sample,
statistic=np.mean,
method='percentile',
bootstrap_conf_level=0.95,
number_of_bootstrap_samples=10000,
plot=True
)
print(f"Mean estimate: {result['statistic_value']:.3f}")
print(f"95% CI: [{result['confidence_interval'][0]:.3f}, {result['confidence_interval'][1]:.3f}]")
# Advanced: BCa (Bias-Corrected and Accelerated) bootstrap
bca_result = fb.one_sample_bootstrap(
sample,
method='bca',
statistic=np.median,
plot=True
)
```
### Two-Sample Comparison
Compare two groups with various statistics:
```python
import fastbootstrap as fb
import numpy as np
# A/B test data
control = np.random.normal(0.25, 0.1, 800) # 25% conversion rate
treatment = np.random.normal(0.28, 0.1, 800) # 28% conversion rate
# Test difference in means
result = fb.two_sample_bootstrap(
control,
treatment,
statistic=fb.difference_of_mean,
number_of_bootstrap_samples=10000,
plot=True
)
print(f"Difference in conversion rates: {result['statistic_value']:.1%}")
print(f"P-value: {result['p_value']:.4f}")
print(f"Significant: {'Yes' if result['p_value'] < 0.05 else 'No'}")
# Test percentage change
percent_result = fb.two_sample_bootstrap(
control,
treatment,
statistic=fb.percent_change_of_mean
)
print(f"Percentage change: {percent_result['statistic_value']:.1%}")
```
### Spotify-Style Bootstrap
Fast quantile-based bootstrap using binomial sampling:
```python
import fastbootstrap as fb
import numpy as np
# Revenue data (heavy-tailed distribution)
control_revenue = np.random.lognormal(3, 1, 1000)
treatment_revenue = np.random.lognormal(3.1, 1, 1000)
# Compare medians (50th percentile)
result = fb.spotify_two_sample_bootstrap(
control_revenue,
treatment_revenue,
q1=0.5, # Median
q2=0.5,
plot=True
)
print(f"Median difference: ${result['statistic_value']:.2f}")
print(f"P-value: {result['p_value']:.4f}")
# Compare different quantiles
p90_result = fb.spotify_two_sample_bootstrap(
control_revenue,
treatment_revenue,
q1=0.9, # 90th percentile
q2=0.9
)
print(f"90th percentile difference: ${p90_result['statistic_value']:.2f}")
```
### Power Analysis & Simulation
Comprehensive statistical power analysis:
```python
import numpy as np
import fastbootstrap as fb
# Simulate experiment data
control = np.random.normal(100, 20, 500)
treatment = np.random.normal(110, 20, 500) # 10% effect size
# Power analysis
power_result = fb.power_analysis(
control,
treatment,
number_of_experiments=1000,
plot=True
)
print("Power Analysis Results:")
print(f"Statistical Power: {power_result['power_summary']['statistical_power']:.3f}")
print(f"Type I Error Rate: {power_result['power_summary']['type_i_error_rate']:.3f}")
print(f"Effect Size: {power_result['power_summary']['treatment_mean'] - power_result['power_summary']['control_mean']:.1f}")
# A/A test validation (should show ~5% false positive rate)
aa_result = fb.aa_test_simulation(
np.concatenate([control, treatment]),
number_of_experiments=2000
)
print(f"A/A Test False Positive Rate: {aa_result['type_i_error_rate']:.3f}")
```
### Quantile-Quantile Analysis
```python
import numpy as np
import fastbootstrap as fb
# Simulate experiment data
control = np.random.exponential(scale=1 / 0.001, size=n)
treatment = np.random.exponential(scale=1 / 0.00101, size=n)
# Quantile-quantile bootstrap analysis
fb.quantile_bootstrap_plot(control, treatment, n_step=1000)
```
### Custom Statistics
Bootstrap with simple custom statistical functions:
```python
import numpy as np
import fastbootstrap as fb
# Simple custom statistics
def max_difference(x, y):
"""Difference in maximum values."""
return np.max(y) - np.max(x)
def range_ratio(x, y):
"""Ratio of ranges."""
range_x = np.max(x) - np.min(x)
range_y = np.max(y) - np.min(y)
return range_y / range_x
def mean_ratio(x, y):
"""Ratio of means."""
return np.mean(y) / np.mean(x)
# Apply custom statistics
control = np.random.normal(50, 10, 300)
treatment = np.random.normal(55, 12, 300)
# Test different custom statistics
max_result = fb.two_sample_bootstrap(control, treatment, statistic=max_difference)
range_result = fb.two_sample_bootstrap(control, treatment, statistic=range_ratio)
ratio_result = fb.two_sample_bootstrap(control, treatment, statistic=mean_ratio)
print(f"Max Difference: {max_result['statistic_value']:.2f}")
print(f"Range Ratio: {range_result['statistic_value']:.3f}")
print(f"Mean Ratio: {ratio_result['statistic_value']:.3f}")
```
### Unified Bootstrap Interface
Automatic method selection based on input:
```python
import numpy as np
import fastbootstrap as fb
# One-sample (automatic detection)
sample = np.random.gamma(2, 2, 400)
result = fb.bootstrap(sample, statistic=np.mean, method='bca')
# Two-sample (automatic detection)
control = np.random.normal(0, 1, 300)
treatment = np.random.normal(0.3, 1, 300)
result = fb.bootstrap(control, treatment)
# Spotify-style (automatic detection)
result = fb.bootstrap(control, treatment, spotify_style=True, q=0.5)
```
## ⚡ Performance Benchmarks
Performance benchmarks on Apple Silicon M1 Pro (results may vary by system):
### Standard Configuration (n=1,000, bootstrap=10,000)
| Method | Time (seconds) | Bootstrap/sec |
|--------|----------------|---------------|
| Spotify One Sample | 0.001 | 19,717,384 |
| Spotify Two Sample | 0.001 | 9,099,065 |
| One Sample Basic | 0.219 | 45,685 |
| One Sample Percentile | 0.224 | 44,601 |
| Two Sample Standard | 0.230 | 43,471 |
| One Sample Studentized | 0.234 | 42,752 |
| One Sample Bca | 0.243 | 41,201 |
| Poisson Bootstrap | 0.298 | 33,581 |
### Key Performance Insights
- **Fastest Method**: Spotify One Sample (0.001s) - optimized quantile-based approach
- **Multithreading**: Leverages joblib for parallel bootstrap sample generation across CPU cores
- **Parallel Processing**: Automatically scales to utilize all available CPU cores for optimal performance
- **Memory Efficient**: O(n) space complexity with minimal memory overhead for large datasets
- **Vectorized Operations**: NumPy-optimized computations for maximum throughput
- **Scalability**: Linear scaling with sample size and bootstrap iterations, sublinear with CPU cores
## 🔧 API Reference
### Core Functions
#### `bootstrap(control, treatment=None, **kwargs)`
Unified bootstrap interface with automatic method selection.
#### `one_sample_bootstrap(sample, **kwargs)`
Single-sample bootstrap for confidence intervals.
#### `two_sample_bootstrap(control, treatment, **kwargs)`
Two-sample bootstrap for group comparisons.
#### `spotify_one_sample_bootstrap(sample, q=0.5, **kwargs)`
Fast quantile bootstrap using binomial sampling.
#### `spotify_two_sample_bootstrap(control, treatment, q1=0.5, q2=0.5, **kwargs)`
Fast two-sample quantile comparison.
### Parameters
| Parameter | Type | Default | Description |
|-----------|------|---------|-------------|
| `bootstrap_conf_level` | float | 0.95 | Confidence level (0-1) |
| `number_of_bootstrap_samples` | int | 10000 | Bootstrap iterations |
| `method` | str | 'percentile' | Bootstrap method |
| `statistic` | callable | `np.mean` | Statistical function |
| `seed` | int | 42 | Random seed |
| `plot` | bool | False | Generate plots |
### Bootstrap Methods
- **percentile**: Basic percentile method
- **bca**: Bias-corrected and accelerated
- **basic**: Basic bootstrap
- **studentized**: Studentized bootstrap
### Statistical Functions
- `difference_of_mean`, `difference_of_median`, `difference_of_std`
- `percent_change_of_mean`, `percent_change_of_median`
- `percent_difference_of_mean`, `percent_difference_of_median`
---
<div align="center">
**[⭐ Star us on GitHub](https://github.com/timofeytkachenko/fastbootstrap)** • **[📖 Full Documentation](https://nbviewer.org/github/timofeytkachenko/fastbootstrap/blob/main/bootstrap_experiment.ipynb)**
</div>
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"description": "# FastBootstrap\n\n<div align=\"center\">\n\n**\u26a1 Fast Python implementation of statistical bootstrap methods**\n\n[](https://badge.fury.io/py/fastbootstrap)\n[](https://www.python.org/downloads/release/python-3120/)\n[](https://opensource.org/licenses/MIT)\n[](https://github.com/psf/black)\n\n*High-performance statistical bootstrap with parallel processing and comprehensive method support*\n\n[Installation](#installation) \u2022 [Quick Start](#quick-start) \u2022 [Examples](#examples) \u2022 [Performance](#performance) \u2022 [API](#api-reference)\n\n</div>\n\n---\n\n## \ud83d\ude80 Features\n\n- **Multiple Bootstrap Methods**: Percentile, BCa, Basic, Studentized, Spotify-style, and Poisson bootstrap\n- **High Performance**: Parallel processing with joblib, optimized NumPy operations\n- **Comprehensive Statistics**: Confidence intervals, p-values, effect sizes, power analysis, quantile-quantile analysis\n- **Flexible API**: Unified interface with method auto-selection\n- **Rich Visualizations**: Built-in plotting with matplotlib and plotly\n- **Production Ready**: Extensive error handling, type hints\n\n## \ud83d\udce6 Installation\n\n```bash\npip install fastbootstrap\n```\n\n### \ud83d\udee0\ufe0f Development Setup\n\n```bash\ngit clone https://github.com/timofeytkachenko/fastbootstrap.git\ncd fastbootstrap\npip install -e \".[dev]\"\npre-commit install\n```\n\n## \ud83c\udfaf Quick Start\n\n```python\nimport numpy as np\nimport fastbootstrap as fb\n\n# Generate sample data\nnp.random.seed(42)\ncontrol = np.random.normal(100, 15, 1000) # Control group\ntreatment = np.random.normal(105, 15, 1000) # Treatment group (+5% effect)\n\n# Two-sample bootstrap test\nresult = fb.two_sample_bootstrap(control, treatment, plot=True)\nprint(f\"P-value: {result['p_value']:.4f}\")\nprint(f\"Effect size: {result['statistic_value']:.2f}\")\nprint(f\"95% CI: [{result['confidence_interval'][0]:.2f}, {result['confidence_interval'][1]:.2f}]\")\n```\n\n## \ud83d\udcca Examples\n\n### One-Sample Bootstrap\n\nEstimate confidence intervals for a single sample statistic:\n\n```python\nimport fastbootstrap as fb\nimport numpy as np\n\n# Sample data\nsample = np.random.exponential(2, 500)\n\n# Basic percentile bootstrap\nresult = fb.one_sample_bootstrap(\n sample,\n statistic=np.mean,\n method='percentile',\n bootstrap_conf_level=0.95,\n number_of_bootstrap_samples=10000,\n plot=True\n)\n\nprint(f\"Mean estimate: {result['statistic_value']:.3f}\")\nprint(f\"95% CI: [{result['confidence_interval'][0]:.3f}, {result['confidence_interval'][1]:.3f}]\")\n\n# Advanced: BCa (Bias-Corrected and Accelerated) bootstrap\nbca_result = fb.one_sample_bootstrap(\n sample,\n method='bca',\n statistic=np.median,\n plot=True\n)\n```\n\n\n\n\n### Two-Sample Comparison\n\nCompare two groups with various statistics:\n\n```python\nimport fastbootstrap as fb\nimport numpy as np\n\n# A/B test data\ncontrol = np.random.normal(0.25, 0.1, 800) # 25% conversion rate\ntreatment = np.random.normal(0.28, 0.1, 800) # 28% conversion rate\n\n# Test difference in means\nresult = fb.two_sample_bootstrap(\n control,\n treatment,\n statistic=fb.difference_of_mean,\n number_of_bootstrap_samples=10000,\n plot=True\n)\n\nprint(f\"Difference in conversion rates: {result['statistic_value']:.1%}\")\nprint(f\"P-value: {result['p_value']:.4f}\")\nprint(f\"Significant: {'Yes' if result['p_value'] < 0.05 else 'No'}\")\n\n# Test percentage change\npercent_result = fb.two_sample_bootstrap(\n control,\n treatment,\n statistic=fb.percent_change_of_mean\n)\nprint(f\"Percentage change: {percent_result['statistic_value']:.1%}\")\n```\n\n\n\n### Spotify-Style Bootstrap\n\nFast quantile-based bootstrap using binomial sampling:\n\n```python\nimport fastbootstrap as fb\nimport numpy as np\n\n# Revenue data (heavy-tailed distribution)\ncontrol_revenue = np.random.lognormal(3, 1, 1000)\ntreatment_revenue = np.random.lognormal(3.1, 1, 1000)\n\n# Compare medians (50th percentile)\nresult = fb.spotify_two_sample_bootstrap(\n control_revenue,\n treatment_revenue,\n q1=0.5, # Median\n q2=0.5,\n plot=True\n)\n\nprint(f\"Median difference: ${result['statistic_value']:.2f}\")\nprint(f\"P-value: {result['p_value']:.4f}\")\n\n# Compare different quantiles\np90_result = fb.spotify_two_sample_bootstrap(\n control_revenue,\n treatment_revenue,\n q1=0.9, # 90th percentile\n q2=0.9\n)\nprint(f\"90th percentile difference: ${p90_result['statistic_value']:.2f}\")\n```\n\n### Power Analysis & Simulation\n\nComprehensive statistical power analysis:\n\n```python\nimport numpy as np\nimport fastbootstrap as fb\n\n# Simulate experiment data\ncontrol = np.random.normal(100, 20, 500)\ntreatment = np.random.normal(110, 20, 500) # 10% effect size\n\n# Power analysis\npower_result = fb.power_analysis(\n control,\n treatment,\n number_of_experiments=1000,\n plot=True\n)\n\nprint(\"Power Analysis Results:\")\nprint(f\"Statistical Power: {power_result['power_summary']['statistical_power']:.3f}\")\nprint(f\"Type I Error Rate: {power_result['power_summary']['type_i_error_rate']:.3f}\")\nprint(f\"Effect Size: {power_result['power_summary']['treatment_mean'] - power_result['power_summary']['control_mean']:.1f}\")\n\n# A/A test validation (should show ~5% false positive rate)\naa_result = fb.aa_test_simulation(\n np.concatenate([control, treatment]),\n number_of_experiments=2000\n)\nprint(f\"A/A Test False Positive Rate: {aa_result['type_i_error_rate']:.3f}\")\n```\n\n\n\n### Quantile-Quantile Analysis\n\n```python\nimport numpy as np\nimport fastbootstrap as fb\n\n# Simulate experiment data\ncontrol = np.random.exponential(scale=1 / 0.001, size=n)\ntreatment = np.random.exponential(scale=1 / 0.00101, size=n)\n\n# Quantile-quantile bootstrap analysis\nfb.quantile_bootstrap_plot(control, treatment, n_step=1000)\n```\n\n\n\n### Custom Statistics\n\nBootstrap with simple custom statistical functions:\n\n```python\nimport numpy as np\nimport fastbootstrap as fb\n\n# Simple custom statistics\ndef max_difference(x, y):\n \"\"\"Difference in maximum values.\"\"\"\n return np.max(y) - np.max(x)\n\ndef range_ratio(x, y):\n \"\"\"Ratio of ranges.\"\"\"\n range_x = np.max(x) - np.min(x)\n range_y = np.max(y) - np.min(y)\n return range_y / range_x\n\ndef mean_ratio(x, y):\n \"\"\"Ratio of means.\"\"\"\n return np.mean(y) / np.mean(x)\n\n# Apply custom statistics\ncontrol = np.random.normal(50, 10, 300)\ntreatment = np.random.normal(55, 12, 300)\n\n# Test different custom statistics\nmax_result = fb.two_sample_bootstrap(control, treatment, statistic=max_difference)\nrange_result = fb.two_sample_bootstrap(control, treatment, statistic=range_ratio)\nratio_result = fb.two_sample_bootstrap(control, treatment, statistic=mean_ratio)\n\nprint(f\"Max Difference: {max_result['statistic_value']:.2f}\")\nprint(f\"Range Ratio: {range_result['statistic_value']:.3f}\")\nprint(f\"Mean Ratio: {ratio_result['statistic_value']:.3f}\")\n```\n\n### Unified Bootstrap Interface\n\nAutomatic method selection based on input:\n\n```python\nimport numpy as np\nimport fastbootstrap as fb\n\n# One-sample (automatic detection)\nsample = np.random.gamma(2, 2, 400)\nresult = fb.bootstrap(sample, statistic=np.mean, method='bca')\n\n# Two-sample (automatic detection)\ncontrol = np.random.normal(0, 1, 300)\ntreatment = np.random.normal(0.3, 1, 300)\nresult = fb.bootstrap(control, treatment)\n\n# Spotify-style (automatic detection)\nresult = fb.bootstrap(control, treatment, spotify_style=True, q=0.5)\n```\n\n## \u26a1 Performance Benchmarks\n\nPerformance benchmarks on Apple Silicon M1 Pro (results may vary by system):\n\n### Standard Configuration (n=1,000, bootstrap=10,000)\n\n| Method | Time (seconds) | Bootstrap/sec |\n|--------|----------------|---------------|\n| Spotify One Sample | 0.001 | 19,717,384 |\n| Spotify Two Sample | 0.001 | 9,099,065 |\n| One Sample Basic | 0.219 | 45,685 |\n| One Sample Percentile | 0.224 | 44,601 |\n| Two Sample Standard | 0.230 | 43,471 |\n| One Sample Studentized | 0.234 | 42,752 |\n| One Sample Bca | 0.243 | 41,201 |\n| Poisson Bootstrap | 0.298 | 33,581 |\n\n### Key Performance Insights\n\n- **Fastest Method**: Spotify One Sample (0.001s) - optimized quantile-based approach\n- **Multithreading**: Leverages joblib for parallel bootstrap sample generation across CPU cores\n- **Parallel Processing**: Automatically scales to utilize all available CPU cores for optimal performance\n- **Memory Efficient**: O(n) space complexity with minimal memory overhead for large datasets\n- **Vectorized Operations**: NumPy-optimized computations for maximum throughput\n- **Scalability**: Linear scaling with sample size and bootstrap iterations, sublinear with CPU cores\n\n## \ud83d\udd27 API Reference\n\n### Core Functions\n\n#### `bootstrap(control, treatment=None, **kwargs)`\nUnified bootstrap interface with automatic method selection.\n\n#### `one_sample_bootstrap(sample, **kwargs)`\nSingle-sample bootstrap for confidence intervals.\n\n#### `two_sample_bootstrap(control, treatment, **kwargs)`\nTwo-sample bootstrap for group comparisons.\n\n#### `spotify_one_sample_bootstrap(sample, q=0.5, **kwargs)`\nFast quantile bootstrap using binomial sampling.\n\n#### `spotify_two_sample_bootstrap(control, treatment, q1=0.5, q2=0.5, **kwargs)`\nFast two-sample quantile comparison.\n\n### Parameters\n\n| Parameter | Type | Default | Description |\n|-----------|------|---------|-------------|\n| `bootstrap_conf_level` | float | 0.95 | Confidence level (0-1) |\n| `number_of_bootstrap_samples` | int | 10000 | Bootstrap iterations |\n| `method` | str | 'percentile' | Bootstrap method |\n| `statistic` | callable | `np.mean` | Statistical function |\n| `seed` | int | 42 | Random seed |\n| `plot` | bool | False | Generate plots |\n\n### Bootstrap Methods\n\n- **percentile**: Basic percentile method\n- **bca**: Bias-corrected and accelerated\n- **basic**: Basic bootstrap\n- **studentized**: Studentized bootstrap\n\n### Statistical Functions\n\n- `difference_of_mean`, `difference_of_median`, `difference_of_std`\n- `percent_change_of_mean`, `percent_change_of_median`\n- `percent_difference_of_mean`, `percent_difference_of_median`\n\n---\n\n<div align=\"center\">\n\n**[\u2b50 Star us on GitHub](https://github.com/timofeytkachenko/fastbootstrap)** \u2022 **[\ud83d\udcd6 Full Documentation](https://nbviewer.org/github/timofeytkachenko/fastbootstrap/blob/main/bootstrap_experiment.ipynb)**\n\n</div>\n",
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