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Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modelling. (English) Zbl 1091.62009

Bayesian estimation of the parameters \(\alpha>0\) and \(\beta>0\) of a Generalized Pareto Distribution (GPD) with density \[ f_{\alpha,\beta}(y)=(\alpha/\beta) \left( 1+y/\beta \right)^{-\alpha-1}, \quad y\geq 0, \] by an i.i.d. sample is considered. A quasi conjugate prior is constructed based on the representation of the GPD PDF as a mixture of exponential densities with Gamma mixing distribution. A Markov chain Monte Carlo procedure with Gibbs sampler for posterior calculations is described. Results of simulations and applications to real data sets are considered.

MSC:

62F15 Bayesian inference
62G32 Statistics of extreme values; tail inference
62F10 Point estimation
65C40 Numerical analysis or methods applied to Markov chains

Software:

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References:

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