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<p>We consider an explicit expression of the EM algorithm for Cauchy and its related distributions. The main idea is developed by making use of the exponential distribution structure, from which a general estimator function is then derived. The explicit forms of the EM algorithm for the Cauchy, log-Cauchy and another Cauchy distributions are derived as examples. We also derive explicit EM update equations for a skew-<i>t</i> distribution, as well as its finite mixture and regression models. An efficient acceleration for the EM algorithm is proposed. Illustrative examples of the mixture and regression models are also given.</p>

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A simple EM algorithm for Cauchy and its related distributions: efficient acceleration and applications to a skew-t distribution and its regression model

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Toshihiro Abe,
  • Masahiro Kuroda

摘要

We consider an explicit expression of the EM algorithm for Cauchy and its related distributions. The main idea is developed by making use of the exponential distribution structure, from which a general estimator function is then derived. The explicit forms of the EM algorithm for the Cauchy, log-Cauchy and another Cauchy distributions are derived as examples. We also derive explicit EM update equations for a skew-t distribution, as well as its finite mixture and regression models. An efficient acceleration for the EM algorithm is proposed. Illustrative examples of the mixture and regression models are also given.