B1591
Title: On the bivariate Farlie-Gumbel-Morgenstern distribution with alternative composite exponential-Pareto marginals
Authors: Adrian Baca - Ovidius University of Constanta, Romania (Romania) [presenting]
Catalina Bolance - University of Barcelona (Spain)
Raluca Vernic - Ovidius University of Constanta (Romania)
Abstract: Two-component spliced (or composite) distributions have been intensively studied in the univariate case in connection to data exhibiting skewness to the right and extreme values, often providing a better fit on the right tail than classical right-skewed distributions. Such distributions are defined from different distributions on distinct contiguous intervals, with the right tail distribution of heavy-tailed type (usually Pareto). Extending spliced distributions to the bivariate setting is an open problem. Thus, a bivariate Farlie-Gumbel-Morgenstern distribution with composite exponential-Pareto marginals is proposed to capture extreme events. Some properties of this bivariate distribution are presented. Since, for this distribution, the estimation is not obvious due to the marginal unknown thresholds (where the exponential changes to Pareto), an estimation procedure is discussed. This procedure is illustrated on two real data samples of bivariate claims costs collected from an auto insurance portfolio. The proposed distribution provides a good fit to both data sets, the estimated marginal distributions being considered with and without the continuity condition at the threshold of the composite exponential-Pareto densities.
