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Competing risks driven by Mittag-Leffler distributions, under copula and time transformed exponential model

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Abstract

We consider a stochastic model for competing risks involving the Mittag-Leffler distribution, inspired by fractional random growth phenomena. We prove the independence between the time to failure and the cause of failure, and investigate some properties of the related hazard rates and ageing notions. We also face the general problem of identifying the underlying distribution of latent failure times when their joint distribution is expressed in terms of copulas and the time transformed exponential model. The special case concerning the Mittag-Leffler distribution is approached by means of numerical treatment. We finally adapt the proposed model to the case of a random number of independent competing risks. This leads to certain mixtures of Mittag-Leffler distributions, whose parameters are estimated through the method of moments for fractional moments.

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Acknowledgments

This research is partially supported by GNCS-INdAM and Regione Campania (Legge 5). The authors thank the anonymous referee for various useful comments.

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  1. Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Antonio Di Crescenzo & Alessandra Meoli

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  1. Antonio Di Crescenzo
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  2. Alessandra Meoli
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Correspondence to Antonio Di Crescenzo.

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Di Crescenzo, A., Meoli, A. Competing risks driven by Mittag-Leffler distributions, under copula and time transformed exponential model. Ricerche mat 66, 361–381 (2017). https://doi.org/10.1007/s11587-016-0304-x

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  • DOI: https://doi.org/10.1007/s11587-016-0304-x

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