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Related Experiment Videos

Polynomial probability distribution estimation using the method of moments.

Joakim Munkhammar1, Lars Mattsson2, Jesper Rydén3

  • 1BEESG, Department of Engineering Sciences/Uppsala University, Uppsala, Sweden.

Plos One
|April 11, 2017
PubMed
Summary
This summary is machine-generated.

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This study introduces a straightforward method for approximating probability density functions (PDFs) using polynomial expansions derived from statistical moments. This technique offers a practical alternative when standard distributions are unsuitable, aiding in complex calculations like convolutions.

Area of Science:

  • Statistics
  • Applied Mathematics
  • Computational Physics

Background:

  • Traditional probability density function (PDF) approximations often rely on established distribution families or series expansions like Gram-Charlier.
  • These methods may not be suitable for all datasets or complex analytical tasks.

Purpose of the Study:

  • To present a novel algorithmic procedure for estimating Nth-degree polynomial approximations of probability density functions (PDFs).
  • To demonstrate the applicability and advantages of this method compared to traditional approaches.

Main Methods:

  • The procedure utilizes the method of moments, deriving polynomial approximations from N statistical moments.
  • An algorithmic setup ensures rigor and practical applicability.
  • The method was tested on Normal, Log-Normal, Weibull, bimodal Weibull distributions, household electricity usage data, and the Smoluchowski equation.

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Main Results:

  • Polynomial PDF approximations were successfully generated for various distributions and a real-world dataset.
  • The proposed method demonstrated comparable or superior performance to Gram-Charlier expansions.
  • The approach simplifies the calculation of distribution convolutions by converting them into polynomial integrals.

Conclusions:

  • The developed procedure offers a simple yet effective alternative for PDF approximation, especially when conventional methods fail.
  • This method is particularly advantageous for computational tasks involving distribution convolutions and approximating solutions to complex equations like the Smoluchowski equation.