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<p>The paper presents a numerical method for obtaining maximum likelihood estimates (MLEs) of the three-parameter Pearson type VII distribution with a diagonal information matrix (PJ distribution). This distribution is recommended as a general model for the errors of large-sample observations. The algorithm for obtaining MLEs of the PJ distribution using a stepwise method, which does not require differentiation of the likelihood function, is described. A software implementation for the stepwise computation of the MLEs of the PJ distribution parameters in C++ is provided, along with results demonstrating its application to determine these estimates from the residual error distribution data of laser observations of artificial Earth satellites obtained within the framework of the international MERIT project.</p>

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Software Implementation of a Numerical Method for Obtaining Maximum Likelihood Estimates of Parameters of the Jeffreys Modification of the Pearson Type VII Distribution

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • J. V. Dzhun,
  • A. M. Yasinsky,
  • A. V. Shportko,
  • L. Ya. Solovei

摘要

The paper presents a numerical method for obtaining maximum likelihood estimates (MLEs) of the three-parameter Pearson type VII distribution with a diagonal information matrix (PJ distribution). This distribution is recommended as a general model for the errors of large-sample observations. The algorithm for obtaining MLEs of the PJ distribution using a stepwise method, which does not require differentiation of the likelihood function, is described. A software implementation for the stepwise computation of the MLEs of the PJ distribution parameters in C++ is provided, along with results demonstrating its application to determine these estimates from the residual error distribution data of laser observations of artificial Earth satellites obtained within the framework of the international MERIT project.