Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios
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 s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2021-07-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1025 |
| _version_ | 1818380054711762944 |
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| author | Hossein Nadeb Hamzeh Torabi |
| author_facet | Hossein Nadeb Hamzeh Torabi |
| author_sort | Hossein Nadeb |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T02:12:35Z |
| format | Article |
| id | doaj.art-b01075cb3b404dc988e0ef3e9c934ea4 |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-12-14T02:12:35Z |
| publishDate | 2021-07-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-b01075cb3b404dc988e0ef3e9c934ea42022-12-21T23:20:44ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2021-07-0150310.17713/ajs.v50i3.1025Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent PortfoliosHossein Nadeb0Hamzeh Torabi1Dept. of Statistics, Yazd University, Yazd, IranDept. of Statistics, Yazd UniversityThe 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.https://www.ajs.or.at/index.php/ajs/article/view/1025 |
| spellingShingle | Hossein Nadeb Hamzeh Torabi Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios Austrian Journal of Statistics |
| title | Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios |
| title_full | Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios |
| title_fullStr | Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios |
| title_full_unstemmed | Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios |
| title_short | Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios |
| title_sort | stochastic comparisons of the smallest claim amounts from two sets of independent portfolios |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1025 |
| work_keys_str_mv | AT hosseinnadeb stochasticcomparisonsofthesmallestclaimamountsfromtwosetsofindependentportfolios AT hamzehtorabi stochasticcomparisonsofthesmallestclaimamountsfromtwosetsofindependentportfolios |