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A method of moments to estimate bivariate survival functions: the copula approach

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  • Silvia Angela Osmetti

    (Department of Statistical Science - Università Cattolica del Sacro Cuore - Milan, Italy)

  • Paola Maddalena Chiodini

    (Department of Statistics - Università degli Studi Milano Bicocca - Milan, Italy)

Abstract

In this paper we discuss the problem on parametric and non arametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. We generalize this model by the copula and different marginal distributions to construct several bivariate survival functions. The cumulative distribution functions are not absolutely continuous and they unknown parameters are often not be obtained in explicit form. In order to estimate the parameters we propose an easy procedure based on the moments. This method consist in two steps: in the first step we estimate only the parameters of marginal distributions and in the second step we estimate only the copula parameter. This procedure can be used to estimate the parameters of complex survival functions in which it is difficult to find an explicit expression of the mixed moments. Moreover it is preferred to the maximum likelihood one for its simplex mathematic form; in particular for distributions whose maximum likelihood parameters estimators can not be obtained in explicit form.

Suggested Citation

  • Silvia Angela Osmetti & Paola Maddalena Chiodini, 2011. "A method of moments to estimate bivariate survival functions: the copula approach," Statistica, Department of Statistics, University of Bologna, vol. 71(4), pages 469-488.
    • Handle: RePEc:bot:rivsta:v:71:y:2011:i:4:p:469-488
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    Cited by:

    1. Ehab Mohamed Almetwally & Hiba Zeyada Muhammed & El-Sayed A. El-Sherpieny, 2020. "Bivariate Weibull Distribution: Properties and Different Methods of Estimation," Annals of Data Science, Springer, vol. 7(1), pages 163-193, March.
    2. Hanan Haj Ahmad & Ehab M. Almetwally & Dina A. Ramadan, 2023. "Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach," Mathematics, MDPI, vol. 11(9), pages 1-23, May.

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