Some Notes for Two Generalized Trigonometric Families of Distributions
The paper deals with two general families of cumulative distribution functions based on arctangent function. We provide analysis of the error of the best one-sided Hausdorff approximation for some special cases of these families. We obtain precious estimates for the value of the Hausdorff distance t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/4/149 |
| _version_ | 1797436888323194880 |
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| author | Maria T. Vasileva |
| author_facet | Maria T. Vasileva |
| author_sort | Maria T. Vasileva |
| collection | DOAJ |
| description | The paper deals with two general families of cumulative distribution functions based on arctangent function. We provide analysis of the error of the best one-sided Hausdorff approximation for some special cases of these families. We obtain precious estimates for the value of the Hausdorff distance that can be used as an additional criterion in practice. Further, the family of recurrence generated adaptive functions is constructed and investigated. All new results are illustrated with suitable numerical experiments. Simple dynamic software modules show applicability of Hausdorff approximation. |
| first_indexed | 2024-03-09T11:10:05Z |
| format | Article |
| id | doaj.art-6bf10235f0b540d2b8c485b806c4c0d9 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T11:10:05Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-6bf10235f0b540d2b8c485b806c4c0d92023-12-01T00:48:10ZengMDPI AGAxioms2075-16802022-03-0111414910.3390/axioms11040149Some Notes for Two Generalized Trigonometric Families of DistributionsMaria T. Vasileva0Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, BulgariaThe paper deals with two general families of cumulative distribution functions based on arctangent function. We provide analysis of the error of the best one-sided Hausdorff approximation for some special cases of these families. We obtain precious estimates for the value of the Hausdorff distance that can be used as an additional criterion in practice. Further, the family of recurrence generated adaptive functions is constructed and investigated. All new results are illustrated with suitable numerical experiments. Simple dynamic software modules show applicability of Hausdorff approximation.https://www.mdpi.com/2075-1680/11/4/149generated familytrigonometric distributionHausdorff distanceHeaviside step functionupper and lower boundsrecurrent family |
| spellingShingle | Maria T. Vasileva Some Notes for Two Generalized Trigonometric Families of Distributions Axioms generated family trigonometric distribution Hausdorff distance Heaviside step function upper and lower bounds recurrent family |
| title | Some Notes for Two Generalized Trigonometric Families of Distributions |
| title_full | Some Notes for Two Generalized Trigonometric Families of Distributions |
| title_fullStr | Some Notes for Two Generalized Trigonometric Families of Distributions |
| title_full_unstemmed | Some Notes for Two Generalized Trigonometric Families of Distributions |
| title_short | Some Notes for Two Generalized Trigonometric Families of Distributions |
| title_sort | some notes for two generalized trigonometric families of distributions |
| topic | generated family trigonometric distribution Hausdorff distance Heaviside step function upper and lower bounds recurrent family |
| url | https://www.mdpi.com/2075-1680/11/4/149 |
| work_keys_str_mv | AT mariatvasileva somenotesfortwogeneralizedtrigonometricfamiliesofdistributions |