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<p>Univariate and bivariate circular data are very frequently reported with values in a discrete set. This is sometimes due to rounding prior to reporting, or it may be a direct result of the experimental design employed in gathering the data. For example, data on directions are frequently reported as values on an equally spaced grid on the interval <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13171_2025_424_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\([0,2\pi )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. But the models used to analyze and fit the data are almost universally continuous models. In this paper we will introduce and survey an array of discrete models which might more appropriately be used to analyze such data.</p>

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Circular and Toroidal Families of Discrete Distributions

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • Ashis SenGupta,
  • Barry C. Arnold

摘要

Univariate and bivariate circular data are very frequently reported with values in a discrete set. This is sometimes due to rounding prior to reporting, or it may be a direct result of the experimental design employed in gathering the data. For example, data on directions are frequently reported as values on an equally spaced grid on the interval \([0,2\pi )\) [ 0 , 2 π ) . But the models used to analyze and fit the data are almost universally continuous models. In this paper we will introduce and survey an array of discrete models which might more appropriately be used to analyze such data.