| Title:
|
Some distribution results on generalized ballot problems (English) |
| Author:
|
Saran, Jagdish |
| Author:
|
Sen, Kanwar |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1985 |
| Pages:
|
157-165 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that in a ballot candidate $A$ scores $a$ votes and candidate $B$ scores $b$ votes and that all possible $\left(\matrix {a+b} \\ a \endmatrix \right)$ voting sequences are equally probable. Denote by $\alpha_r$ and by $\beta_r$ the number of votes registered for $A$ and for $B$, respectively, among the first $r$ votes recorded, $r=1, \dots, a+b$. The purpose of this paper is to derive, for $a\geq b-c$, the probability distributions of the random variables defined as the number of subscripts $r=1, \dots, a+b$ for which (i) $\alpha_r=\beta_r-c$, (ii) $\alpha_r=\beta_r-c$ but $\alpha_{r-1}=\beta_{r-1}-c\pm 1$, (iii) $\alpha_r=\beta_r-c$ but $\alpha_{r-1}=\beta_{r-1}-c\pm 1$ and $\alpha_{r+1}=\beta_{r+1}-c\pm 1$, where $c=0,\pm 1, \pm 2, \dots$. (English) |
| Keyword:
|
ballot problem |
| MSC:
|
60C05 |
| MSC:
|
60E99 |
| MSC:
|
60J15 |
| idZBL:
|
Zbl 0575.60008 |
| idMR:
|
MR0789857 |
| DOI:
|
10.21136/AM.1985.104138 |
| . |
| Date available:
|
2008-05-20T18:27:12Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104138 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
