Fractional integrals in the matrix-variate cases and connection to statistical distributions
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Bibliographic record
Abstract
This study examines the possible extensions of the classical fractional integral operators of scalar functions of scalar variables to the matrix-variate cases and establishes their connections to statistical distribution theory. Real-valued scalar functions of matrix argument, where the argument matrix is real and positive definite, are used in the extensions. Riemann–Liouville left-sided and right-sided fractional integral operators, Saigo integral operators and Liouville integral operators are given matrix-variate extensions. A connection is established between Riemann–Liouville fractional integrals to the distributions of sum and difference of two real positive independently distributed random variables. Some fractional integrals are also given interpretations as incomplete integrals and fractions of the total probability in statistical distribution theory.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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