A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data
The idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces a novel...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1356 |
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| author | Moustafa Salem Walid Emam Yusra Tashkandy Mohamed Ibrahim M. Masoom Ali Hafida Goual Haitham M. Yousof |
| author_facet | Moustafa Salem Walid Emam Yusra Tashkandy Mohamed Ibrahim M. Masoom Ali Hafida Goual Haitham M. Yousof |
| author_sort | Moustafa Salem |
| collection | DOAJ |
| description | The idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces a novel asymmetric model for assessing risks under a skewed claims dataset. The new distribution is also employed for both censored and uncensored validation testing. Four estimation methods, maximum likelihood, ordinary least squares, L-Moment, and Anderson Darling, were used for the risk assessment and analysis. To explain the exposure to risk within actuarial claims data, we introduced five crucial indicators, namely value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess losses. A numerical and graphical analysis is presented to assess the actuarial risk. Furthermore, the article discusses a newly developed Rao Robson Nikulin statistic for censored and uncensored validation testing. The validation testing also involved the insurance claims dataset. |
| first_indexed | 2024-03-11T00:36:02Z |
| format | Article |
| id | doaj.art-40423d4a424d4f649c162465463a9a07 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:02Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-40423d4a424d4f649c162465463a9a072023-11-18T21:33:56ZengMDPI AGSymmetry2073-89942023-07-01157135610.3390/sym15071356A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical DataMoustafa Salem0Walid Emam1Yusra Tashkandy2Mohamed Ibrahim3M. Masoom Ali4Hafida Goual5Haitham M. Yousof6Department of Applied Statistics, Damanhour University, Damanhour 22511, EgyptDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta 34517, EgyptDepartment of Mathematical Sciences, Ball State University, Muncie, IN 47306, USALaboratory of Probability and Statistics LaPS, Department of Mathematics, Badji Mokhtar Annaba University, Annaba 23000, AlgeriaDepartment of Statistics, Mathematics and Insurance, Benha University, Benha 13511, EgyptThe idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces a novel asymmetric model for assessing risks under a skewed claims dataset. The new distribution is also employed for both censored and uncensored validation testing. Four estimation methods, maximum likelihood, ordinary least squares, L-Moment, and Anderson Darling, were used for the risk assessment and analysis. To explain the exposure to risk within actuarial claims data, we introduced five crucial indicators, namely value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess losses. A numerical and graphical analysis is presented to assess the actuarial risk. Furthermore, the article discusses a newly developed Rao Robson Nikulin statistic for censored and uncensored validation testing. The validation testing also involved the insurance claims dataset.https://www.mdpi.com/2073-8994/15/7/1356skewed claim dataCullen–FreyL-momentLomax distributionrisk indicatorsrisk analysis |
| spellingShingle | Moustafa Salem Walid Emam Yusra Tashkandy Mohamed Ibrahim M. Masoom Ali Hafida Goual Haitham M. Yousof A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data Symmetry skewed claim data Cullen–Frey L-moment Lomax distribution risk indicators risk analysis |
| title | A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data |
| title_full | A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data |
| title_fullStr | A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data |
| title_full_unstemmed | A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data |
| title_short | A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data |
| title_sort | new lomax extension properties risk analysis censored and complete goodness of fit validation testing under left skewed insurance reliability and medical data |
| topic | skewed claim data Cullen–Frey L-moment Lomax distribution risk indicators risk analysis |
| url | https://www.mdpi.com/2073-8994/15/7/1356 |
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