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New results for the Marshall-Olkin family of distributions

  • Emilio Gómez-Déniz EMAIL logo , M. E. Ghitany and D. K. Al-Mutairi
Published/Copyright: August 14, 2024
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Abstract

The Marshall-Olkin family of probability distributions has been the inspiration of numerous research publications in the field of probability distributions. In this paper, we present several new properties of this family. In particular, we focus on stochastic orders, stress-strength reliability, Lorenz and the Leimkhuler curves, compounding, and integrated tail distribution. Two applications related to Lorenz curves and ruin theory are finally presented.

MSC 2010: 62F10; 60E15; 62F05

Acknowledgement

The authors would like to thank the anonymous referees for valuable comments and suggestions which improved the presentation of this paper.

EGD was partially funded by grant PID2021-127989OB-I00 (Ministerio de Economía y Competitividad, Spain) and by grant TUR-RETOS2022-075 (Ministerio de Industria, Comercio y Turismo).

  1. Communicated by Gejza Wimmer

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Received: 2023-06-22
Accepted: 2023-12-06
Published Online: 2024-08-14
Published in Print: 2024-08-27

© 2024 Mathematical Institute Slovak Academy of Sciences

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