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Order Statistics and Record Values Moments from the Topp-Leone Lomax Distribution with Applications to Entropy

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Abstract

In this paper, we derive the exact expressions, as well as recurrence relations, for the single and product moments of the order statistics (OSs) and record values of the Topp-Leone Lomax (TLLo) distribution proposed by Oguntunde et al. (Wirel Person Commun 109:349–360, 2019). In addition, we study the corresponding L-moments. We estimate the distribution parameters through these L-moments and compare our results to those obtained in other models. Subsequently, motivated by the study of Okorie and Nadarajah (Wirel Person Commun 115:589–596, 2020), we fit the flood level data to the TLLo distribution. Finally, we reveal a relationship between the entropy and the upper and lower record values, as well as OSs.

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Data Availability

https://doi.org/10.1080/00401706.1973.10489124.

Code Availability

We are using the softwere MATHEMATICA an R to calculate the numeical values.

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Funding

This research received no external funding.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science and Technology, Vishwakarma University, Pune, 411 048, India

    Mahfooz Alam

  2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    Haroon M. Barakat

  3. Department of Mathematics, College of Science, Qassim University, 51452, Buraydah, Saudi Arabia

    Hassan S. Bakouch

  4. Department of Mathematics, Tanta University, Tanta, 31111, Egypt

    Hassan S. Bakouch

  5. Department of Mathematics, LMNO, Université de Caen, Campus II, Science 3, 14032, Caen, France

    Christophe Chesneau

Authors
  1. Mahfooz Alam
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  2. Haroon M. Barakat
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  3. Hassan S. Bakouch
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  4. Christophe Chesneau
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Contributions

MA proposed the concept of the paper and calculated the existing results. HMB contributed in writing original draft preparation and determined the existing results. HSB contributes to the methodology and concepts for the e existing results. CC, HMB and HSB performed revision and improved the quality of the draft. All authors have read and agreed to the published version of the manuscrit.

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Correspondence to Mahfooz Alam.

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Alam, M., Barakat, H.M., Bakouch, H.S. et al. Order Statistics and Record Values Moments from the Topp-Leone Lomax Distribution with Applications to Entropy. Wireless Pers Commun 135, 2209–2227 (2024). https://doi.org/10.1007/s11277-024-11136-w

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