Some new results involving residual Renyi's information measure for $ k $-record values

Mansour Shrahili; Mansour Shrahili

doi:10.3934/math.2024649

AIMS Mathematics

2024, Volume 9, Issue 5: 13313-13335. doi: 10.3934/math.2024649

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Research article

Some new results involving residual Renyi's information measure for $ k $-record values

Mansour Shrahili ^,

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 26 February 2024 Revised: 22 March 2024 Accepted: 27 March 2024 Published: 10 April 2024
MSC : 94A08, 62P99

This article dealt with further properties of the Renyi entropy and the residual Renyi entropy of $ k $-record values. First, we discussed the Renyi entropy order and its connection with the usual stochastic and dispersive orders. We then addressed the monotonicity properties of the residual Renyi entropy of $ k $-records, focusing on the aging properties of the component lifetimes. We also expressed the residual $ n $th upper $ k $-records in terms of Renyi entropy when the first dataset exceeded a certain threshold, and then studied various properties of the given formula. Finally, we conducted a parametric estimation of the Renyi entropy of the $ n $th upper $ k $-records. The estimation was performed using both real COVID-19 data and simulated data.
- information theory,
- $ k $-record values,
- Renyi entropy,
- residual Renyi entropy,
- stochastic orders
Citation: Mansour Shrahili. Some new results involving residual Renyi's information measure for $ k $-record values[J]. AIMS Mathematics, 2024, 9(5): 13313-13335. doi: 10.3934/math.2024649

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Abstract

This article dealt with further properties of the Renyi entropy and the residual Renyi entropy of $ k $-record values. First, we discussed the Renyi entropy order and its connection with the usual stochastic and dispersive orders. We then addressed the monotonicity properties of the residual Renyi entropy of $ k $-records, focusing on the aging properties of the component lifetimes. We also expressed the residual $ n $th upper $ k $-records in terms of Renyi entropy when the first dataset exceeded a certain threshold, and then studied various properties of the given formula. Finally, we conducted a parametric estimation of the Renyi entropy of the $ n $th upper $ k $-records. The estimation was performed using both real COVID-19 data and simulated data.

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