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The generalized Pearson family of distributions and explicit representation of the associated density functions

Author

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  • Serge B. Provost
  • Hossein Zareamoghaddam
  • S. Ejaz Ahmed
  • Hyung-Tae Ha

Abstract

A moment-based density approximation technique that is based on a generalization of Pearson’s system of frequency curves is introduced in this paper. More specifically, the derivative of the logarithm of a continuous density function is expressed as a ratio of polynomials whose coefficients are determined by solving a linear system, and a simple representation of the resulting density function is provided. Additionally, a result relating a sample to its moments is stated and derived. It is then explained that, when used in conjunction with sample moments, the methodology being herein advocated can be utilized for the purpose of modeling data sets, irrespective of their size. Several illustrative examples are presented.

Suggested Citation

  • Serge B. Provost & Hossein Zareamoghaddam & S. Ejaz Ahmed & Hyung-Tae Ha, 2022. "The generalized Pearson family of distributions and explicit representation of the associated density functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(16), pages 5590-5606, August.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:16:p:5590-5606
    DOI: 10.1080/03610926.2020.1843680
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