MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

Bivariate Composite distributions with Pareto tail for modeling bivariate data

  • 1 Ovidius University of Constanta, Romania
  • 2 University of Barcelona, Spain

Abstract

Financial data or insurance claim data often exhibit skewness to the right and extreme values, so that classical right skewed distributions like Exponential, Gamma, Weibull or Lognormal fail to capture their behavior. However, built from different distributions on distinct contiguous intervals, two-component spliced (or composite) models often provide a better fit on the right tail, especially since the right tail distribution is considered to be of heavy-tailed type (usually Pareto). In this work, we introduce two bivariate composite distributions defined from a bivariate type I Pareto distribution for values larger than some thresholds, and a bivariate distribution less heavy-tailed on the complementary domain. We present some properties of the new distributions and discuss an estimation method, illustrated on a real data set from insurance.

Keywords

References

  1. K. Cooray, M.M. Ananda, Modeling actuarial data with a composite Lognormal-Pareto model. Scand. Actuar. J., 2005(5), 321-334 (2005).
  2. A. Badea, C. Bolance, R. Vernic, On the bivariate composite Gumbel-Pareto Distribution. Stats, 5(4), 948-969 (2022).
  3. S. Kotz, N. Balakrishnan, N.L. Johnson, Continuous multivariate distributions, Vol. 1: Models and applications. Wiley (2004).
  4. Bolancé, C.; Guillen, M.; Pelican, E.; Vernic, R. Skewed bivariate models and nonparametric estimation for the CTE risk measure. Insur. Math. Econ. 2008, 43, 386–393.
  5. Bahraoui, Z.; Bolancé, C.; Pelican, E.; Vernic, R. On the bivariate Sarmanov distribution and copula. An application on insurance data using truncated marginal distributions. SORT 2015, 39, 209–230.

Article full text

Download PDF