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Abstract <p>In this note, the dispersion of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5069_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\)</EquationSource> <!--MMStat2570002Balakrishnan-m3--> </InlineEquation>-Poisson distribution is studied. It is specifically shown that this distribution is over-dispersed when <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5069_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt;q&lt;1\)</EquationSource> <!--MMStat2570002Balakrishnan-m4--> </InlineEquation> and under-dispersed when <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5069_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;q&lt;\infty\)</EquationSource> <!--MMStat2570002Balakrishnan-m5--> </InlineEquation>.</p>

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A Note on the Dispersion of \(\boldsymbol{q}\)-Poisson Distribution

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • N. Balakrishnan,
  • Ch. A. Charalambides

摘要

Abstract

In this note, the dispersion of \(q\) -Poisson distribution is studied. It is specifically shown that this distribution is over-dispersed when \(0<q<1\) and under-dispersed when \(1<q<\infty\) .