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Distortion representations of multivariate distributions

Author

Listed:
  • Jorge Navarro

    (Universidad de Murcia Campus de Espinardo)

  • Camilla Calì

    (Dipartimento di Biologia. Università di Napoli Federico II Via Cintia)

  • Maria Longobardi

    (Dipartimento di Biologia. Università di Napoli Federico II Via Cintia)

  • Fabrizio Durante

    (Dipartimento di Scienze dell’Economia, Università del Salento Lecce)

Abstract

The univariate distorted distributions were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later, they were also applied to represent distributions of order statistics, coherent systems, proportional hazard rate and proportional reversed hazard rate models, etc. In this paper we extend this concept to the multivariate setup. We show that, in some cases, they are a valid alternative to the copula representation, especially when the marginal distributions may not be easily handled. Several examples illustrate the applications of such representations in statistical modeling. They include the study of paired (dependent) ordered data, joint residual lifetimes, order statistics and coherent systems

Suggested Citation

  • Jorge Navarro & Camilla Calì & Maria Longobardi & Fabrizio Durante, 2022. "Distortion representations of multivariate distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 925-954, October.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:4:d:10.1007_s10260-021-00613-2
    DOI: 10.1007/s10260-021-00613-2
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    References listed on IDEAS

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    8. Jorge Navarro & Camilla Calì, 2019. "Inactivity times of coherent systems with dependent components under periodical inspections," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 871-892, May.
    9. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
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    13. Sordo, Miguel A. & Castaño-Martínez, Antonia & Pigueiras, Gema, 2016. "A family of premium principles based on mixtures of TVaRs," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 397-405.
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    Cited by:

    1. Arriaza, Antonio & Navarro, Jorge & Ortega-Jiménez, Patricia, 2024. "Risk times in mission-oriented systems," LIDAM Discussion Papers ISBA 2024017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Jorge Navarro & Franco Pellerey & Julio Mulero, 2022. "On sums of dependent random lifetimes under the time-transformed exponential model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 879-900, December.
    3. Jorge Navarro & Francesco Buono, 2023. "Predicting future failure times by using quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 543-576, July.

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