A discrete extension of the Burr-Hatke distribution: Generalized hypergeometric functions, different inference techniques, simulation ranking with modeling and analysis of sustainable count data

Khaled M. Alqahtani; Mahmoud El-Morshedy; Hend S. Shahen; Mohamed S. Eliwa; Khaled M. Alqahtani; Mahmoud El-Morshedy; Hend S. Shahen; Mohamed S. Eliwa

doi:10.3934/math.2024458

AIMS Mathematics

2024, Volume 9, Issue 4: 9394-9418. doi: 10.3934/math.2024458

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A discrete extension of the Burr-Hatke distribution: Generalized hypergeometric functions, different inference techniques, simulation ranking with modeling and analysis of sustainable count data

1.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Department of Mathematics, Misr Institute for Computer Science, Egypt
3.
Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 27 December 2023 Revised: 03 February 2024 Accepted: 20 February 2024 Published: 07 March 2024
MSC : 62E99, 62E15

The intertwining relationship between sustainability and discrete probability distributions found its significance in decision-making processes and risk assessment frameworks. Count data modeling and its practical applications have gained attention in numerous research studies. This investigation focused on a particular discrete distribution characterized by a single parameter obtained through the survival discretization method. Statistical attributes of this distribution were accurately explicated using generalized hypergeometric functions. The unveiled characteristics highlighted its suitability for analyzing data displaying "right-skewed" asymmetry and possessing extended "heavy" tails. Its failure rate function effectively addressed scenarios marked by a consistent decrease in rates. Furthermore, it proved to be a valuable tool for probabilistic modeling of over-dispersed data. The study introduced various estimation methods such as maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, maximum likelihood, least-squares, weighted least-squares, percentile, and Cramer-Von-Mises, offering comprehensive explanations. A ranking simulation study was conducted to evaluate the performance of these estimators, employing ranking techniques to identify the most effective estimator across different sample sizes. Finally, real-world sustainability engineering and medical datasets were analyzed to demonstrate the significance and application of the newly introduced model.
- statistical model,
- survival discretization technique,
- generalized hypergeometric function,
- estimation methods,
- computer simulation,
- sustainable extreme count data
Citation: Khaled M. Alqahtani, Mahmoud El-Morshedy, Hend S. Shahen, Mohamed S. Eliwa. A discrete extension of the Burr-Hatke distribution: Generalized hypergeometric functions, different inference techniques, simulation ranking with modeling and analysis of sustainable count data[J]. AIMS Mathematics, 2024, 9(4): 9394-9418. doi: 10.3934/math.2024458

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Abstract

The intertwining relationship between sustainability and discrete probability distributions found its significance in decision-making processes and risk assessment frameworks. Count data modeling and its practical applications have gained attention in numerous research studies. This investigation focused on a particular discrete distribution characterized by a single parameter obtained through the survival discretization method. Statistical attributes of this distribution were accurately explicated using generalized hypergeometric functions. The unveiled characteristics highlighted its suitability for analyzing data displaying "right-skewed" asymmetry and possessing extended "heavy" tails. Its failure rate function effectively addressed scenarios marked by a consistent decrease in rates. Furthermore, it proved to be a valuable tool for probabilistic modeling of over-dispersed data. The study introduced various estimation methods such as maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, maximum likelihood, least-squares, weighted least-squares, percentile, and Cramer-Von-Mises, offering comprehensive explanations. A ranking simulation study was conducted to evaluate the performance of these estimators, employing ranking techniques to identify the most effective estimator across different sample sizes. Finally, real-world sustainability engineering and medical datasets were analyzed to demonstrate the significance and application of the newly introduced model.

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