Open AccessStochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios
Author(s) -
Hossein Nadeb,
Hamzeh Torabi
Publication year - 2021
Publication title -
österreichische zeitschrift für statistik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.342
H-Index - 9
ISSN - 1026-597X
DOI - 10.17713/ajs.v50i3.1025
Subject(s) - actuary , mathematics , stochastic ordering , scale (ratio) , discrete mathematics , actuarial science , mathematical economics , economics , physics , quantum mechanics
The aim of this paper is detecting the ordering properties of the smallest claim amounts arising from two sets of independent heterogeneous portfolios in insurance. First, we prove a general theorem that it presents some sufficient conditions in the sense of the hazard rate ordering to compare the smallest claim amounts from two batches of independent heterogeneous portfolios. Then, we show that the exponentiated scale model as a famous model and the Harris family satisfy the sufficient conditions of the proven general theorem. Also, to illustrate our results, some used models in actuary are numerically applied.