Scholarlink

<p>An urn contains a known number of balls of two different colors. We describe the random variable counting the smallest number of draws needed in order to observe at least <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\,c\,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mspace width="0.166667em" /> <mi>c</mi> <mspace width="0.166667em" /> </mrow> </math></EquationSource> </InlineEquation> of both colors when sampling without replacement for a prespecified, positive integer value of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\,c\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mspace width="0.166667em" /> <mi>c</mi> </mrow> </math></EquationSource> </InlineEquation>. This distribution is the finite sample analogy to the maximum negative binomial distribution described by Zhang et al. [<CitationRef CitationID="CR14">14</CitationRef>]. We describe the modes, approximating distributions, and estimation of the contents of the urn. This distribution is used to estimate the sample size for planning a stratified clinical trial.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Maximum Negative Hypergeometric Distribution

  • 期刊论文

  • 发表日期：

    2025年9月28日

查看全文
  • Chang Yu,
  • K Prishwalko,
  • Ondrej Blaha,
  • Michael Kane,
  • Wei Wei,
  • Denise Esserman,
  • Daniel Zelterman

摘要

An urn contains a known number of balls of two different colors. We describe the random variable counting the smallest number of draws needed in order to observe at least \(\,c\,\) c of both colors when sampling without replacement for a prespecified, positive integer value of \(\,c\) c . This distribution is the finite sample analogy to the maximum negative binomial distribution described by Zhang et al. [14]. We describe the modes, approximating distributions, and estimation of the contents of the urn. This distribution is used to estimate the sample size for planning a stratified clinical trial.