On the Extreme Value -Function
Abstract
:1. Introduction and Preliminaries
2. The Extreme Value -Function
General Behavior
3. Relationship between the Extreme Value -Function and the H-Function
Relationship between the Extreme Value -Function and Higher-Level Hypergeometric Functions
- : The second inequality indicates that . By combining this result with the limitation that , it is easy to see that as long as , both inequalities are satisfied.
- : The second inequality indicates that , which implies that by simply taking and , all inequalities are satisfied.
4. Special Cases
- H-function
- Gamma function
5. Series Representation
6. Applications to Extreme Value Statistical Theory
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Random Variable | ||||||
---|---|---|---|---|---|---|
Exponential | 0 | 0 | 0 | 0 | 0 | |
Weibull | 0 | 1 | 0 | k | ||
Rayleigh | 0 | 1 | 0 | 2 | 1 | |
Nakagami-m | 0 | 1 | 0 | 2 | ||
Generalized Gamma | 0 | 1 | 0 | p | ||
Half-Normal | 0 | 1 | 0 | 2 | 0 | |
Fréchet | 0 | 1 | 0 |
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Rathie, P.N.; Ozelim, L.C.d.S.M.; Quintino, F.; Fonseca, T.A.d.
On the Extreme Value
Rathie PN, Ozelim LCdSM, Quintino F, Fonseca TAd.
On the Extreme Value
Rathie, Pushpa Narayan, Luan Carlos de Sena Monteiro Ozelim, Felipe Quintino, and Tiago A. da Fonseca.
2023. "On the Extreme Value
Rathie, P. N., Ozelim, L. C. d. S. M., Quintino, F., & Fonseca, T. A. d.
(2023). On the Extreme Value