.. _index:

ToFUL — Tool for Uncertainty Learning
======================================

.. image:: https://static.streamlit.io/badges/streamlit_badge_black_white.svg
   :target: https://toful1.streamlit.app/
   :alt: Live App

.. image:: https://img.shields.io/badge/python-3.9+-blue.svg
   :target: https://www.python.org/downloads/
   :alt: Python 3.9+

.. image:: https://img.shields.io/badge/License-MIT-yellow.svg
   :target: https://opensource.org/licenses/MIT
   :alt: MIT License

.. image:: https://readthedocs.org/projects/toful-rtd/badge/?version=latest
   :target: https://toful-rtd.readthedocs.io/en/latest/
   :alt: Documentation Status

----

**ToFUL** is an interactive web application and Python computation engine for
computing statistical moments of probability distributions — both discrete and
continuous — with rigorous numerical methods, convergence acceleration, and
real-time validation.

.. code-block:: text

   E[(X − a)ʳ]   ←  the r-th moment of X about point a

Whether you are a student exploring probability theory, a researcher verifying
distributional properties, or a data scientist needing quick moment calculations,
ToFUL provides accurate results with transparent methodology.

**Try it now:** `toful1.streamlit.app <https://toful1.streamlit.app/>`_

----

.. toctree::
   :maxdepth: 1
   :caption: Getting Started

   getting-started/installation
   getting-started/quickstart
   getting-started/input-syntax

.. toctree::
   :maxdepth: 2
   :caption: User Guide

   user-guide/discrete-rv
   user-guide/continuous-rv
   user-guide/mathematical-functions
   user-guide/precision-settings
   user-guide/interpreting-results

.. toctree::
   :maxdepth: 2
   :caption: Examples

   examples/discrete-distributions
   examples/continuous-distributions
   examples/advanced-examples

.. toctree::
   :maxdepth: 2
   :caption: Theory & Background

   theory/statistical-moments
   theory/raw-vs-central
   theory/skewness-kurtosis
   theory/convergence

.. toctree::
   :maxdepth: 2
   :caption: API Reference

   api-reference/core
   api-reference/toful-parser

.. toctree::
   :maxdepth: 2
   :caption: Troubleshooting

   troubleshooting/common-errors
   troubleshooting/debugging-functions
   troubleshooting/convergence-issues

.. toctree::
   :maxdepth: 1
   :caption: Development

   contributing/index
   changelog

----

Indices and tables
==================

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`