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Summary
This summary is machine-generated.

This study introduces a new web-calculator for bivariate and trivariate probability distributions, addressing a gap in current AI and statistical tools. The accessible online calculator aids in understanding complex multivariate probability for data scientists and AI learners.

Keywords:
AI/MLcopulacumulative distributioneducationmultivariate distributionprobability densityprobability distributionstatistics

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Area of Science:

  • Artificial Intelligence
  • Statistics
  • Data Science

Background:

  • Mathematical modeling, probability estimation, and statistical inference are crucial for artificial intelligence (AI).
  • Existing tools primarily focus on univariate probability distributions, limiting advanced AI applications.
  • Multivariate distributions are essential for complex statistical inference and AI decision-making.

Purpose of the Study:

  • To present a novel web-calculator for computing and visualizing bivariate and trivariate probability distributions.
  • To bridge the gap in readily available tools for multivariate probability analysis.
  • To support data scientists, STEM instructors, and AI learners in their educational and research endeavors.

Main Methods:

  • Exploration of methods for computing joint bivariate and trivariate probability densities, including Gaussian copula modeling.
  • Development of an interactive web application using HTML5 and JavaScript for platform independence and scalability.
  • Visualization of parallels between mathematical formulations, computational implementation, and graphical representations of multivariate probability density and cumulative distribution functions.

Main Results:

  • Validation of the web application through testing multivariate copula models under various experimental conditions.
  • Demonstration of the accuracy and reliability of estimated multivariate probability densities and distribution function values.
  • Successful construction, implementation, and utilization of the multivariate probability calculators.

Conclusions:

  • The developed web application provides a valuable resource for calculating and visualizing multivariate probability distributions.
  • The tool is freely available online, promoting broader access to advanced statistical and AI concepts.
  • This resource can significantly assist in the education and research related to multivariate statistics and AI.