Constant Rate Distributions on Partially Ordered Sets
We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting ([0,∞),≤) that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment results and re...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/675754 |
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| _version_ | 1849305398166683648 |
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| author | Kyle Siegrist |
| author_facet | Kyle Siegrist |
| author_sort | Kyle Siegrist |
| collection | DOAJ |
| description | We consider probability distributions with constant rate on partially
ordered sets, generalizing distributions in the usual reliability setting
([0,∞),≤) that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment
results and results concerning ladder variables and point processes. We
concentrate mostly on discrete posets, particularly posets whose graphs
are rooted trees. We pose some questions on the existence of constant
rate distributions for general discrete posets. |
| format | Article |
| id | doaj-art-078540ebae52440ab89895aeee6743fd |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-078540ebae52440ab89895aeee6743fd2025-08-20T03:55:28ZengWileyJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/675754675754Constant Rate Distributions on Partially Ordered SetsKyle Siegrist0Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USAWe consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting ([0,∞),≤) that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment results and results concerning ladder variables and point processes. We concentrate mostly on discrete posets, particularly posets whose graphs are rooted trees. We pose some questions on the existence of constant rate distributions for general discrete posets.http://dx.doi.org/10.1155/2010/675754 |
| spellingShingle | Kyle Siegrist Constant Rate Distributions on Partially Ordered Sets Journal of Probability and Statistics |
| title | Constant Rate Distributions on Partially Ordered Sets |
| title_full | Constant Rate Distributions on Partially Ordered Sets |
| title_fullStr | Constant Rate Distributions on Partially Ordered Sets |
| title_full_unstemmed | Constant Rate Distributions on Partially Ordered Sets |
| title_short | Constant Rate Distributions on Partially Ordered Sets |
| title_sort | constant rate distributions on partially ordered sets |
| url | http://dx.doi.org/10.1155/2010/675754 |
| work_keys_str_mv | AT kylesiegrist constantratedistributionsonpartiallyorderedsets |