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 import DistFit

# Generate or load your data
rng = np.random.default_rng(42)
data = rng.beta(2, 5, 1000)  # Example: skewed data

# Fit a Bézier distribution (MSE objective, projected-gradient solver)
fitter = DistFit(data, n=5)  # 5 control segments
bezier_rv, mse = fitter.fit(method='mse', algorithm='projected_gradient')

# Use the fitted distribution
samples = bezier_rv.random(10000)      # Generate new samples
q90 = bezier_rv.quantile(0.90)         # 90th percentile
mean = bezier_rv.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 import DistFit, Convolver

# Fit two distributions
rv1, _ = DistFit(data1, n=4).fit(method='mse', algorithm='projected_gradient')
rv2, _ = DistFit(data2, n=4).fit(method='mse', algorithm='projected_gradient')

# Compute their sum: Z = X + Y
convolver = Convolver([rv1, rv2])
sum_mc, _ = convolver.convolve(n_sims=10000, rng=42)

Documentation

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:

method='mse' returns (bezierv, mse). method='mle' returns (bezierv, nll).

Citation

If you use bezierv in your research, please cite the accompanying paper (forthcoming on arXiv):

@article{leiva2026bezierv,
  title   = {Computational Framework for {B\'{e}zier} Distributions},
  author  = {Leiva, Esteban and Medaglia, Andr\'{e}s L. and Zuluaga, Luis F.},
  year    = {2026},
  note    = {Forthcoming on arXiv}
}

License

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