Rényi entropy on k-records and its applications in characterizing distributions

References

• David HA, Nagaraja HN. Order statistics. New York: Wiley; 2003.
   Google Scholar
• Chandler K. The distribution and frequency of record values. J R Stat Soc Ser B (Methodol). 1952;14:220–228.
   Google Scholar
• Dziubdziela W, Kopociński B. Limiting properties of the kth record values. Appl Math. 1976;2(15):187–190.
   Google Scholar
• Minimol S, Thomas PY. On some properties of Makeham distribution using generalized record values and its characterizations. Braz J Probab Stat. 2013;27(4):487–501.
   Web of Science ®Google Scholar
• Minimol S, Thomas PY. On characterization of Gompertz distribution by generalized record values. J Stat Theory Appl. 2014;13(1):38–45.
   Google Scholar
• Paul J, Thomas PY. On generalized upper (k) record values from Weibull distribution. Statistica. 2015;75(3):313.
   Google Scholar
• Paul J, Thomas PY. On generalized (k) record values from Pareto distribution. Aligarh J Statist. 2016;36(1):63–78.
   Google Scholar
• Arnold BC, Balakrishnan N, Nagaraja HN. Records. New York: John Wiley & Sons; 1998.
   Google Scholar
• Ahsanullah M. Record values – theory and applications. Maryland: University Press of America; 2004.
   Google Scholar
• Thomas PY, Philip A, Veena TG. Characterization of bivariate distributions using concomitants of generalized (k) record values. Statistica. 2014;74(4):431–446.
   Google Scholar
• Jose J, Thomas PY. A new bivariate distribution with extreme value type I and Burr type XII distributions as marginals. J Kerala Stat Assoc. 2018;29:1–24.
   Google Scholar
• Thomas PY, Jose J. A new bivariate distribution with Rayleigh and Lindley distributions as marginals. J Stat Theory Pract. 2020;14:Article ID 28.
   PubMed Web of Science ®Google Scholar
• Thomas PY, Jose J. On Weibull–Burr impounded bivariate distribution. Japan J Statist Data Sci. 2020;4(1):73–105.
   Google Scholar
• Madadi M, Tata M. Shannon information in k-records. Comm Statist Theory Methods. 2014;43(15):3286–3301.
   Web of Science ®Google Scholar
• Shannon CE. A mathematical theory of communication. Bell Syst Tech J. 1948;27(3):379–423.
   Google Scholar
• Sathar EIA, Jose J. Past extropy of k-records. Stoch Qual Control. 2020;35(1):25–38.
   Google Scholar
• Jose J, Sathar EIA. Rényi entropy of k-records: properties and applications. REVSTAT. 2020. Accepted for publication.
   Web of Science ®Google Scholar
• Jose J, Sathar EIA. Characterization of exponential distribution using extropy based on lower k-records and its application in testing exponentiality. J Comput Appl Math. 2021. DOI:https://doi.org/10.1016/j.cam.2021.113816
   Web of Science ®Google Scholar
• Jose J, Sathar EIA. Symmetry being tested through simultaneous application of upper and lower k-records in extropy. J Stat Comput Simul. 2021. DOI:https://doi.org/10.1080/00949655.2021.1975283
   Web of Science ®Google Scholar
• Hartley RV. Transmission of information. Bell Syst Tech J. 1928;7(3):535–563.
   Google Scholar
• Rényi A. On measures of entropy and information. In: Proceedings of Fourth Berkely Symposium on Mathematics, Statistics and Probability; 1960; Vol. 1. Berkely (CA): University of California Press; 1961. P. 547–561.
   Google Scholar
• Dong X. The gravity dual of Rényi entropy. Nat Commun. 2016;7(1):1–6.
   Web of Science ®Google Scholar
• Moradpour H, Moosavi S, Lobo I, et al. Thermodynamic approach to holographic dark energy and the Rényi entropy. Eur Phys J C. 2018;78(10):1–6.
   Web of Science ®Google Scholar
• Luo Y, Guo C, You S, et al. A novel perspective of the Kalman filter from the Rényi entropy. Entropy. 2020;22(9):982.
   PubMed Web of Science ®Google Scholar
• Contreras-Reyes JE. Rényi entropy and complexity measure for skew-Gaussian distributions and related families. Physica A. 2015;433:84–91.
   Web of Science ®Google Scholar
• Contreras-Reyes JE, Cortés DD. Bounds on Rényi and Shannon entropies for finite mixtures of multivariate skew-normal distributions: application to swordfish. Entropy. 2016;18(11):382.
   Web of Science ®Google Scholar
• Lu T-C, Grover T. Renyi entropy of chaotic eigenstates. Phys Rev E. 2019;99(3):Article ID 032111.
   Web of Science ®Google Scholar
• Goffman C, Pedrick G. A first course in functional analysis. Vol. 319. New Jersey: American Mathematical Soc; 1965.
   Google Scholar
• Higgins JR. Completeness and basis properties of sets of special functions. New York: Cambridge University Press; 2004.
   Google Scholar
• Fashandi M, Ahmadi J. Characterizations of symmetric distributions based on Rényi entropy. Statist Probab Lett. 2012;82(4):798–804.
   Web of Science ®Google Scholar