bezierv 1.2.0

This package serves as a computational framework for Bézier distributions.

bezierv

Fit smooth Bézier random variables to empirical data

---

Why Bézier Random Variables?

Traditional parametric distributions (normal, exponential, etc.) can be too rigid for real-world data. bezierv bridges the gap between non-parametric and parametric approaches by using Bézier curves to create smooth, flexible distributions that can fit virtually any shape.

Key advantages:

• 📈 Flexible: Fit any continuous distribution shape
• 🎛️ Controllable: Intuitive control points for fine-tuning
• 🔄 Composable: Built-in convolution for sums of random variables
• ⚡ Fast: Multiple efficient fitting algorithms
• 🎨 Visual: Interactive tools for exploration

---

Quick Start

Installation

pip install bezierv

Basic Usage

import numpy as np
from bezierv.classes.distfit import DistFit

# Generate or load your data
data = np.random.beta(2, 5, 1000)  # Example: skewed data

# Fit a Bézier distribution
fitter = DistFit(data, n=5)  # 5 control segments
bezier_rv, mse = fitter.fit(method="projgrad")

# Use the fitted distribution
samples = bezier_rv.random(10000)      # Generate new samples
q90 = bezier_rv.quantile(0.90)         # 90th percentile  
mean = bezier_rv.get_mean()            # Distribution mean
prob = bezier_rv.cdf_x(0.5)            # P(X ≤ 0.5)

# Visualize the fit
bezier_rv.plot_cdf(data)  # Compare with empirical CDF
bezier_rv.plot_pdf()      # Show probability density

Advanced: Convolution of Random Variables

from bezierv.classes.convolver import Convolver

# Fit two distributions
rv1 = DistFit(data1, n=4).fit()[0]
rv2 = DistFit(data2, n=4).fit()[0]

# Compute their sum: Z = X + Y
convolver = Convolver([rv1, rv2])

# Monte Carlo
sum_mc = convolver.convolve(n_sims=10000)

---

Documentation

Resource	Description
📖 User Guide	Complete tutorials and examples
🔧 API Reference	Detailed function documentation
🎮 Interactive Demo	Browser-based curve editor
📚 Tutorials	Step-by-step examples and guides

---

Interactive Tool

Launch an interactive Bézier curve editor in your browser:

from bezierv.classes.bezierv import InteractiveBezierv
from bokeh.plotting import curdoc

# Create interactive editor
editor = InteractiveBezierv(
    controls_x=[0.0, 0.25, 0.75, 1.0],
    controls_z=[0.0, 0.1, 0.9, 1.0]
)

curdoc().add_root(editor.layout)

Then run: bokeh serve --show your_app.py

---

Algorithms

bezierv includes multiple fitting algorithms optimized for different scenarios:

Algorithm
projgrad
projsubgrad
nonlinear
neldermead

License

This project is licensed under the MIT License - see the LICENSE file for details.