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The Arctangent Regression and the Estimation of Parameters of the Cauchy Distribution

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Abstract. Some estimates of the parameters of a nonlinear regression between the variables of X and Y are constructed for the arctangent as a regression function. The obtained estimates are used to evaluate the unknown parameters of the Cauchy distribution. Computer simulations are performed, and the estimates are compared with another estimates such as the quantile ones, maximum liklyhood estimates, and some others. The confidence intervals for parameters of the Cauchy distribution are obtained.

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Authors and Affiliations

  1. Vasyl’ Stus Donetsk National University, Vinnytsia, Ukraine

    Ivan H. Krykun

  2. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slov’yansk, Ukraine

    Ivan H. Krykun

Authors
  1. Ivan H. Krykun
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Correspondence to Ivan H. Krykun.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 2, pp. 196–214 April–June, 2020.

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Krykun, I.H. The Arctangent Regression and the Estimation of Parameters of the Cauchy Distribution. J Math Sci 249, 739–753 (2020). https://doi.org/10.1007/s10958-020-04970-3

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  • DOI: https://doi.org/10.1007/s10958-020-04970-3

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