Asymptotic properties of the number of replications of a paired comparison
A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta fu...
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| Veröffentlicht in: | Journal of applied probability 1974-03, Vol.11 (1), p.43-52 |
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| container_end_page | 52 |
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| container_issue | 1 |
| container_start_page | 43 |
| container_title | Journal of applied probability |
| container_volume | 11 |
| creator | Uppuluri, V. R. R. Blot, W. J. |
| description | A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball. |
| doi_str_mv | 10.2307/3212581 |
| format | Article |
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R.</au><au>Blot, W. J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic properties of the number of replications of a paired comparison</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>1974-03-01</date><risdate>1974</risdate><volume>11</volume><issue>1</issue><spage>43</spage><epage>52</epage><pages>43-52</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><abstract>A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.2307/3212581</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 1974-03, Vol.11 (1), p.43-52 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_crossref_primary_10_2307_3212581 |
| source | Jstor Complete Legacy; JSTOR Mathematics and Statistics |
| subjects | Asymptotic properties Asymptotic value Density distributions DNA Games Generating function Genetic code Mathematical moments Random variables Research Papers Series convergence |
| title | Asymptotic properties of the number of replications of a paired comparison |
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