Conditions on unimodality and logconcavity for densities of coherent systems with an application to Bernstein operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:467

Article

Bieniek, Mariusz¹  Burkschat, Marco²  Rychlik, Tomasz³ 

[1] Marie Curie Sklodowska Univ, Inst Math, Pl Marii Curie Sklodowskiej 1, PL-20031 Lublin, Poland

[2] Rhein Westfal TH Aachen, Inst Stat, D-52056 Aachen, Germany

[3] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

关键词: Unimodality;    Logconcavity;    Signature;    Coherent system;    Variation diminishing property;    Bernstein polynomial;   

DOI  :  10.1016/j.jmaa.2018.07.054

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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