Type-1 Beta Distribution and its Connections to Likelihood Ratio Test
In many cases involving hypothesis testing for parameters in multivariate Gaussian populations and certain other populations, likelihood ratio criteria, or their one-to-one functions, can be expressed in terms of the determinant of a real type-1 beta matrix. In geometrical probability problems, when...
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University of Bologna
2024-12-01
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| Series: | Statistica |
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| Online Access: | https://rivista-statistica.unibo.it/article/view/16837 |
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| author | Nicy Sebastian T. Princy |
| author_facet | Nicy Sebastian T. Princy |
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| description | In many cases involving hypothesis testing for parameters in multivariate Gaussian populations and certain other populations, likelihood ratio criteria, or their one-to-one functions, can be expressed in terms of the determinant of a real type-1 beta matrix. In geometrical probability problems, when the random points are type-1 beta distributed, the volume content of the parallellotope generated by these points is also associated with the determinant of a real type-1 beta matrix. These problems in the corresponding complex domain do not seem to have been discussed in the literature. It is well-known that the determinant of a real type-1 beta matrix can be written as a product of statistically independently distributed real scalar type-1 beta random variables. This paper addresses the general h-th moments of a scalar random variable, in either the real or complex domain, for any arbitrary h. The structure of these moments is quite general, and the paper provides exact distribution results, asymptotic gamma function results, and asymptotic normal results for both the real and complex domains. |
| format | Article |
| id | doaj-art-01a0281b209942c4b19bdd8245364cdd |
| institution | Kabale University |
| issn | 0390-590X 1973-2201 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Bologna |
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| series | Statistica |
| spelling | doaj-art-01a0281b209942c4b19bdd8245364cdd2025-01-09T08:39:06ZengUniversity of BolognaStatistica0390-590X1973-22012024-12-0183215316410.6092/issn.1973-2201/1683715195Type-1 Beta Distribution and its Connections to Likelihood Ratio TestNicy Sebastian0T. Princy1St Thomas College Thrissur, Calicut University, Kerala, IndiaCochin University of Science and Technology, Kerala, IndiaIn many cases involving hypothesis testing for parameters in multivariate Gaussian populations and certain other populations, likelihood ratio criteria, or their one-to-one functions, can be expressed in terms of the determinant of a real type-1 beta matrix. In geometrical probability problems, when the random points are type-1 beta distributed, the volume content of the parallellotope generated by these points is also associated with the determinant of a real type-1 beta matrix. These problems in the corresponding complex domain do not seem to have been discussed in the literature. It is well-known that the determinant of a real type-1 beta matrix can be written as a product of statistically independently distributed real scalar type-1 beta random variables. This paper addresses the general h-th moments of a scalar random variable, in either the real or complex domain, for any arbitrary h. The structure of these moments is quite general, and the paper provides exact distribution results, asymptotic gamma function results, and asymptotic normal results for both the real and complex domains.https://rivista-statistica.unibo.it/article/view/16837likelihood ratio criteriatype-1 beta matrixgeneral structuresreal and complex casesasymptotic chi-squareasymptotic normalexact distribution |
| spellingShingle | Nicy Sebastian T. Princy Type-1 Beta Distribution and its Connections to Likelihood Ratio Test Statistica likelihood ratio criteria type-1 beta matrix general structures real and complex cases asymptotic chi-square asymptotic normal exact distribution |
| title | Type-1 Beta Distribution and its Connections to Likelihood Ratio Test |
| title_full | Type-1 Beta Distribution and its Connections to Likelihood Ratio Test |
| title_fullStr | Type-1 Beta Distribution and its Connections to Likelihood Ratio Test |
| title_full_unstemmed | Type-1 Beta Distribution and its Connections to Likelihood Ratio Test |
| title_short | Type-1 Beta Distribution and its Connections to Likelihood Ratio Test |
| title_sort | type 1 beta distribution and its connections to likelihood ratio test |
| topic | likelihood ratio criteria type-1 beta matrix general structures real and complex cases asymptotic chi-square asymptotic normal exact distribution |
| url | https://rivista-statistica.unibo.it/article/view/16837 |
| work_keys_str_mv | AT nicysebastian type1betadistributionanditsconnectionstolikelihoodratiotest AT tprincy type1betadistributionanditsconnectionstolikelihoodratiotest |