On normality assumptions for claims in insurance

Abstract

The aim of this paper is to discuss effects of deviations from hypothetized normality. Two models are considered, one is the first pension pillar (and we consider here very small samples, which plays some role at start of some pension system or at early phases of it) and second one of modeling for IBNR (here we consider mid-samples). We will show that at early phases of 1st pension pillar in Slovakia the estimation of upper probability of oversizing of critical constant given by Potocký and Stehlík, 2005, fits well. For the case of IBNR reserves, the date given by Stelljes, 2006, are significantly more skewed and thus further research is needed for appropriate modelling of these reserves.

Keywords

• IBNR
• pension pillar
• classical tests of normality
• robust tests of normality
• modified tests of nor­ma­li­ty