Central and Local Limit Theorems for Numbers of the Tribonacci Triangle
In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distributio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/8/880 |
| _version_ | 1797537562018971648 |
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| author | Igoris Belovas |
| author_facet | Igoris Belovas |
| author_sort | Igoris Belovas |
| collection | DOAJ |
| description | In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle. |
| first_indexed | 2024-03-10T12:16:57Z |
| format | Article |
| id | doaj.art-ffe62ad3b9f74f4bb812256b5833c6f7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:16:57Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ffe62ad3b9f74f4bb812256b5833c6f72023-11-21T15:49:38ZengMDPI AGMathematics2227-73902021-04-019888010.3390/math9080880Central and Local Limit Theorems for Numbers of the Tribonacci TriangleIgoris Belovas0Institute of Data Science and Digital Technologies, Vilnius University, LT-04812 Vilnius, LithuaniaIn this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.https://www.mdpi.com/2227-7390/9/8/880tribonacci matrixtriangular arraylimit theoremsrate of convergencegenerating functions |
| spellingShingle | Igoris Belovas Central and Local Limit Theorems for Numbers of the Tribonacci Triangle Mathematics tribonacci matrix triangular array limit theorems rate of convergence generating functions |
| title | Central and Local Limit Theorems for Numbers of the Tribonacci Triangle |
| title_full | Central and Local Limit Theorems for Numbers of the Tribonacci Triangle |
| title_fullStr | Central and Local Limit Theorems for Numbers of the Tribonacci Triangle |
| title_full_unstemmed | Central and Local Limit Theorems for Numbers of the Tribonacci Triangle |
| title_short | Central and Local Limit Theorems for Numbers of the Tribonacci Triangle |
| title_sort | central and local limit theorems for numbers of the tribonacci triangle |
| topic | tribonacci matrix triangular array limit theorems rate of convergence generating functions |
| url | https://www.mdpi.com/2227-7390/9/8/880 |
| work_keys_str_mv | AT igorisbelovas centralandlocallimittheoremsfornumbersofthetribonaccitriangle |