Statistical modelling for a new family of generalized distributions with real data applications

M. E. Bakr; Abdulhakim A. Al-Babtain; Zafar Mahmood; R. A. Aldallal; Saima Khan Khosa; M. M. Abd El-Raouf; Eslam Hussam; Ahmed M. Gemeay; M. E. Bakr; Abdulhakim A. Al-Babtain; Zafar Mahmood; R. A. Aldallal; Saima Khan Khosa; M. M. Abd El-Raouf; Eslam Hussam; Ahmed M. Gemeay

doi:10.3934/mbe.2022404

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 8705-8740. doi: 10.3934/mbe.2022404

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Research article Special Issues

Statistical modelling for a new family of generalized distributions with real data applications

1.
Department of Statistics and Operation Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2.
Government Associate College, Khairpur Tamewali, Bahawalpur, Pakistan
3.
College of Business Administration in Hotat bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
4.
Department of Mathematics and Statistics University of Saskatchewan, Saskatoon, SK, Canada
5.
Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Alexandria, Egypt
6.
Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
7.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Academic Editor: Yong Liu

Received: 19 April 2022 Revised: 03 June 2022 Accepted: 06 June 2022 Published: 16 June 2022

The modern trend in distribution theory is to propose hybrid generators and generalized families using existing algebraic generators along with some trigonometric functions to offer unique, more flexible, more efficient, and highly productive G-distributions to deal with new data sets emerging in different fields of applied research. This article aims to originate an odd sine generator of distributions and construct a new G-family called "The Odd Lomax Trigonometric Generalized Family of Distributions". The new densities, useful functions, and significant characteristics are thoroughly determined. Several specific models are also presented, along with graphical analysis and detailed description. A new distribution, "The Lomax cosecant Weibull" (LocscW), is studied in detail. The versatility, robustness, and competency of the LocscW model are confirmed by applications on hydrological and survival data sets. The skewness and kurtosis present in this model are explained using modern graphical methods, while the estimation and statistical inference are explored using many estimation approaches.
- Lomax distribution,
- T-X transformation,
- odd trigonometric generator,
- stress-strength reliability,
- stochastic ordering,
- order statistics
Citation: M. E. Bakr, Abdulhakim A. Al-Babtain, Zafar Mahmood, R. A. Aldallal, Saima Khan Khosa, M. M. Abd El-Raouf, Eslam Hussam, Ahmed M. Gemeay. Statistical modelling for a new family of generalized distributions with real data applications[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 8705-8740. doi: 10.3934/mbe.2022404

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Abstract

The modern trend in distribution theory is to propose hybrid generators and generalized families using existing algebraic generators along with some trigonometric functions to offer unique, more flexible, more efficient, and highly productive G-distributions to deal with new data sets emerging in different fields of applied research. This article aims to originate an odd sine generator of distributions and construct a new G-family called "The Odd Lomax Trigonometric Generalized Family of Distributions". The new densities, useful functions, and significant characteristics are thoroughly determined. Several specific models are also presented, along with graphical analysis and detailed description. A new distribution, "The Lomax cosecant Weibull" (LocscW), is studied in detail. The versatility, robustness, and competency of the LocscW model are confirmed by applications on hydrological and survival data sets. The skewness and kurtosis present in this model are explained using modern graphical methods, while the estimation and statistical inference are explored using many estimation approaches.

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