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A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters

Indranil Ghosh () and Osborne Banks
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Indranil Ghosh: University of North Carolina
Osborne Banks: University of North Carolina

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 11, 575-604

Abstract: Abstract Several variants of the classical bivariate and multivariate generalized Pareto distributions have been discussed and studied in the literature (see Arnold (1983, Stat. Prob. Lett. 17: 361–368, 1993, 2015), Arnold and Laguna (1977), Ali and Nadarajah (2007), Rootzen and Tajvidi (2006) and the references cited therein). Ali and Nadarajah (2007) studied a truncated version of the most popular long-tailed generalized bivariate Pareto distribution (GBPD, henceforth, in short) involving six parameters. However, not much discussion exists in the current literature on the structural properties as well as on the dependence structure among the parameters in this model. In this paper we re-visit the GBPD and discuss several other new properties. In addition, we study the shape of GBPD for varying choices of the model parameters and subsequently study their interdependence. Also, we provide copula based construction of GBPD and discuss the associated local dependence measures.

Keywords: Generalized Pareto distribution; Ageing property; Stochastic ordering; Bivariate copula; Local dependence function; Primary 62E; Secondary 62F (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-020-00224-z

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