Representative Points from a Mixture of Two Normal Distributions

Yinan Li, Kai Tai Fang, Ping He*, Heng Peng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


In recent years, the mixture of two-component normal distributions (MixN) has attracted considerable interest due to its flexibility in capturing a variety of density shapes. In this paper, we investigate the problem of discretizing a MixN by a fixed number of points under the minimum mean squared error (MSE-RPs). Motivated by the Fang-He algorithm, we provide an effective computational procedure with high precision for generating numerical approximations of MSE-RPs from a MixN. We have explored the properties of the nonlinear system used to generate MSE-RPs and demonstrated the convergence of the procedure. In numerical studies, the proposed computation procedure is compared with the k-means algorithm. From an application perspective, MSE-RPs have potential advantages in statistical inference.Our numerical studies show that MSE-RPs can significantly improve Kernel density estimation.

Original languageEnglish
Article number3952
Issue number21
Early online date24 Oct 2022
Publication statusPublished - Nov 2022

Scopus Subject Areas

  • Computer Science (miscellaneous)
  • Mathematics(all)
  • Engineering (miscellaneous)

User-Defined Keywords

  • Fang-He algorithm
  • k-means algorithm
  • Kernel density estimations
  • mixture of normal distributions
  • representative points


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