beta4dist 0.2.1

A Python package for the Four-Parameter Beta Distribution and Likelihood-Based Estimation

beta4dist

beta4dist is a Python package designed for working with the four-parameter Beta distribution and implementing likelihood-based estimation methods for its parameters. It allows for sampling, parameter fitting, and likelihood-based estimation (LBE) using a flexible four-parameter formulation of the Beta distribution.

Table of Contents

• Description
• Features
• Installation
• Examples
  • Generate Samples
  • Fit the Distribution
  • Test Cases
• Licensing
• References

Description

The goal of beta4dist is to provide an easy-to-use and efficient interface for working with the four-parameter Beta distribution. This package supports the following features:

• Sampling from the four-parameter Beta distribution.
• Fitting the distribution to data using likelihood-based estimation (LBE).
• Implementing various parameter inference techniques for reliable statistical modeling.

The four-parameter Beta distribution extends the standard Beta distribution by introducing location parameters, providing additional flexibility for modeling data confined to finite intervals with skewness and kurtosis. This makes it especially useful in fields like hydrology, environmental science, and reliability engineering.

Features

• Sampling: Generate random samples from the four-parameter Beta distribution.
• Parameter Estimation: Perform likelihood-based estimation for fitting the distribution to observed data.
• Robustness: Ensure that parameter estimates obey the natural restrictions of the distribution.
• Flexible Usage: Suitable for a wide range of applications, including statistical modeling and simulation.

Installation

To install beta4dist, you can use pip from PyPI:

To install the package for the first time:

pip install beta4dist

To upgrade to the latest version:

pip install --upgrade beta4dist

2. Clone the repository from GitHub:

If you prefer to work with the latest code or contribute, you can clone the repository directly from GitHub:

git clone https://github.com/soham39039820/beta4dist.git

After cloning, navigate to the project directory and install it:

cd beta4dist
pip install .

Generate Samples from the Four-Parameter Beta Distribution

You can generate random samples from the four-parameter Beta distribution using the r4beta function:

import beta4dist
from beta4dist.distribution import r4beta

# Define parameters
theta1, theta2 = 0, 1
alpha1, alpha2 = 2.5, 3.0

# Generate 100 samples
samples = r4beta(n=100, theta1=theta1, theta2=theta2, alpha1=alpha1, alpha2=alpha2)

print(samples)

Fit the Four-Parameter Beta Distribution Using Likelihood-Based Estimation

The LBE4beta function allows you to obtain the likelihood-based estimators of the four-parameter Beta distribution to your data. The fit4beta offers an end-to-end interface to fit the distribution to real data, with automatic handling of boundary estimation, internal consistency checks, and feasibility diagnostics.

from beta4dist.beta4_model import LBE4beta, fit4beta

estimates = LBE4beta(data)
print("Estimated Parameters:", estimates)

# Fit and display model diagnostics
fit_results = fit4beta(data)
print("Model Fit Summary:", fit_results)

Example Test Cases

beta4dist includes pre-defined test cases to ensure that the model behaves as expected. You can run these tests using pytest.

Install pytest if you haven't already:

pip install pytest

Run test using:

pytest

Windows users — if pytest is not recognized, try:

"C:\Users\soham\AppData\Roaming\Python\Python310\Scripts\pytest.exe"

Licensing

beta4dist is licensed under the MIT License. See the LICENSE file for more details.

References

For more information on the four-parameter Beta distribution and its applications, please refer to the following publication:

• Paper Title: beta4dist: A Python Package for the Four-Parameter Beta Distribution and Likelihood-Based Estimation
• Authors: Soham Ghosh, Sujay Mukhoti, Pritee Sharma