Conditions on unimodality and logconcavity for densities of coherent systems with an application to Bernstein operators
| Autor: | Tomasz Rychlik, Marco Burkschat, Mariusz Bieniek |
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| Rok vydání: | 2018 |
| Předmět: |
Independent and identically distributed random variables
Distribution (number theory) Component (thermodynamics) Applied Mathematics 010102 general mathematics Probability density function 01 natural sciences Unimodality 010104 statistics & probability Operator (computer programming) Applied mathematics 0101 mathematics Signature (topology) Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 467:863-873 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2018.07.054 |
| Popis: | In this note, the distribution of the lifetime of a coherent system with independent and identically distributed component lifetimes is considered. Conditions yielding unimodality or logconcavity of the density function of the system lifetime are obtained. In the conditions, only assumptions on the density function of the components and on the signature of the system are imposed. The results are illustrated with several examples. Additionally, a problem on preservation of logconcavity under the classical Bernstein operator is solved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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