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Bezierv: A Python Package for Bézier Distributions

Bezierv provides utilities to fit, analyze, sample, and convolve Bézier-based random variables from empirical data. It includes multiple fitting algorithms (projected gradient, projected subgradient, nonlinear (Pyomo/IPOPT), and Nelder–Mead), plus helpers for plotting and Monte Carlo convolution.

Tip: See the API reference for auto-generated docs from the code.

Quickstart

Install your package (editable mode recommended while developing):

pip install bezierv

Fit a Bézier random variable to data with DistFit and sample from it:

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

# Synthetic bounded data
rng = np.random.default_rng(42)
data = rng.beta(2, 5, 1000)  # replace with your data

fitter = DistFit(data, n=5)            # n = degree (n control segments, n+1 control points)
bz, mse = fitter.fit(method="projgrad")  # or: 'nonlinear', 'projsubgrad', 'neldermead'
print("MSE:", mse)

samples = bz.random(10_000, rng=42)     # draw samples via inverse CDF
q90 = bz.quantile(0.90)                 # 90% quantile
print("90% quantile:", q90)

Plot empirical vs. fitted CDF (optional):

bz.plot_cdf(data)       # overlays ECDF and Bézier CDF

Convolution (sum of independent Bézier RVs)

Use Convolver to approximate the sum of several fitted distributions via Monte Carlo, then fit another Bézier RV to the result:

from bezierv.classes.convolver import Convolver
from bezierv.classes.distfit import DistFit

# Fit two Bezier RVs separately (bz1, bz2) ... then:
conv = Convolver([bz, bz])          # example: sum with itself
bz_sum = conv.convolve(n_sims=1_000, rng=123, method="projgrad", n=7)

Plot fitted CDF (optional):

bz_sum.plot_cdf(data)       # overlays ECDF and Bézier CDF

Fitting methods at a glance

  • Projected Gradient (projgrad) – fast and simple; optimizes z controls with projection.
  • Projected Subgradient (projsubgrad) – updates both x and z with projection.
  • Nonlinear (nonlinear) – solves a constrained model via Pyomo (e.g., IPOPT).
  • Nelder–Mead (neldermead) – derivative-free simplex search with penalties.

Next steps