Advances and Applications in Statistics

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A NEW FAMILY OF DISTRIBUTIONS: PROPERTIES AND APPLICATIONS

Authors

  • Ali A. Al-Shomrani
  • Ahmed I. Shawky

Keywords:

Burr XII distribution, maximum likelihood estimation, ordinary and incomplete moments, entropies, quantile function.

DOI:

https://doi.org/10.17654/0972361724015

Abstract

The present study has shown the existence of a novel category of distributions known as the Burr XII general (BXII-G) distribution. The ordinary and incomplete moments, quantile function, entropies (Rényi and Shannon), and order statistics are derived, yielding explicit formulas. The maximum likelihood estimators for the parameters are thoroughly examined. The present discourse concerns examining the Burr XII-log-logistic (BXII-LL) distribution which constitutes a distinctive model within the newly introduced family. Three empirical data sets from real-life scenarios are analyzed to provide a practical demonstration of the suggested family.

Received: October 12, 2023
Accepted: December 29, 2023

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Published

13-01-2024

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Vol. 91 No. 3 (2024)

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A NEW FAMILY OF DISTRIBUTIONS: PROPERTIES AND APPLICATIONS. (2024). Advances and Applications in Statistics , 91(3), 257-300. https://doi.org/10.17654/0972361724015

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