A novel weighted family of probability distributions with applications to world natural gas, oil, and gold reserves

Amal S. Hassan; Najwan Alsadat; Christophe Chesneau; Ahmed W. Shawki; Amal S. Hassan; Najwan Alsadat; Christophe Chesneau; Ahmed W. Shawki

doi:10.3934/mbe.2023880

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19871-19911. doi: 10.3934/mbe.2023880

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Research article

A novel weighted family of probability distributions with applications to world natural gas, oil, and gold reserves

1.
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
2.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
3.
Department of Mathematics, University de Caen Normandie, Campus Ⅱ, Caen 14032, France
4.
Central Agency for Public Mobilization & Statistics (CAPMAS), Cairo, Egypt

Received: 08 July 2023 Revised: 07 September 2023 Accepted: 22 October 2023 Published: 01 November 2023

Recent innovations have focused on the creation of new families that extend well-known distributions while providing a huge amount of practical flexibility for data modeling. Weighted distributions offer an effective approach for addressing model building and data interpretation problems. The main objective of this work is to provide a novel family based on a weighted generator called the length-biased truncated Lomax-generated (LBTLo-G) family. Discussions are held about the characteristics of the LBTLo-G family, including expressions for the probability density function, moments, and incomplete moments. In addition, different measures of uncertainty are determined. We provide four new sub-distributions and investigated their functionalities. Subsequently, a statistical analysis is given. The LBTLo-G family's parameter estimation is carried out using the maximum likelihood technique on the basis of full and censored samples. Simulation research is conducted to determine the parameters of the LBTLo Weibull (LBTLoW) distribution. Four genuine data sets are considered to illustrate the fitting behavior of the LBTLoW distribution. In each case, the application outcomes demonstrate that the LBTLoW distribution can, in fact, fit the data more accurately than other rival distributions.
- weighted distribution,
- incomplete moments,
- Tsallis measure,
- maximum likelihood estimation,
- censored samples
Citation: Amal S. Hassan, Najwan Alsadat, Christophe Chesneau, Ahmed W. Shawki. A novel weighted family of probability distributions with applications to world natural gas, oil, and gold reserves[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19871-19911. doi: 10.3934/mbe.2023880

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Abstract

Recent innovations have focused on the creation of new families that extend well-known distributions while providing a huge amount of practical flexibility for data modeling. Weighted distributions offer an effective approach for addressing model building and data interpretation problems. The main objective of this work is to provide a novel family based on a weighted generator called the length-biased truncated Lomax-generated (LBTLo-G) family. Discussions are held about the characteristics of the LBTLo-G family, including expressions for the probability density function, moments, and incomplete moments. In addition, different measures of uncertainty are determined. We provide four new sub-distributions and investigated their functionalities. Subsequently, a statistical analysis is given. The LBTLo-G family's parameter estimation is carried out using the maximum likelihood technique on the basis of full and censored samples. Simulation research is conducted to determine the parameters of the LBTLo Weibull (LBTLoW) distribution. Four genuine data sets are considered to illustrate the fitting behavior of the LBTLoW distribution. In each case, the application outcomes demonstrate that the LBTLoW distribution can, in fact, fit the data more accurately than other rival distributions.

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