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Atchadé MN, N'bouké MA, Djibril AM, Mutairi AA, Mustafa MS, Hussam E, Alsuhabi H, Nassr SG. A new Topp-Leone Kumaraswamy Marshall-Olkin generated family of distributions with applications. Heliyon 2024; 10:e24001. [PMID: 38298704 PMCID: PMC10828651 DOI: 10.1016/j.heliyon.2024.e24001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2023] [Revised: 12/09/2023] [Accepted: 01/02/2024] [Indexed: 02/02/2024] Open
Abstract
We aim in this paper to propose a novel class of distributions that was created by merging the Topp-Leone distribution and the Generated families of Kumaraswamy and Marshall-Olkin. Its cumulative distribution function characterizes it and includes rational and polynomial functions. In particular, the following desirable properties of the new family are presented: Shannon entropy, order statistics, the quantile power series, and several associated measures and functions. Then, using a specific family member identified before, we create a parametric statistical model with the basic distribution being the inverse exponential distribution. Finally, a thorough investigation has been made to implement this new distribution with three data sets: the glass fibers data set, the glass Alumina data set and the hailing times data set. In comparison to six prominent competitors, the new model performs favorably on all statistical tests and criteria that were examined.
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Affiliation(s)
- Mintodê Nicodème Atchadé
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Republic of Benin
- University of Abomey-Calavi/International Chair in Mathematical Physics and Applications (ICMPA: UNESCO-Chair), 072 BP 50 Cotonou, Republic of Benin
| | - Melchior A.G. N'bouké
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Republic of Benin
| | - Aliou Moussa Djibril
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Republic of Benin
| | - Aned Al Mutairi
- Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
| | | | - Eslam Hussam
- Department of Accounting, College of Business Administration in Hawtat bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
| | - Hassan Alsuhabi
- Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia
| | - Said G. Nassr
- Department of Statistics and Insurance, Faculty of Commerce, Arish University, Al-Arish 45511, Egypt
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Atchadé MN, N’bouké M, Djibril AM, Shahzadi S, Hussam E, Aldallal R, Alshanbari HM, Gemeay AM, El-Bagoury AAH. A New Power Topp-Leone distribution with applications to engineering and industry data. PLoS One 2023; 18:e0278225. [PMID: 36649270 PMCID: PMC9844870 DOI: 10.1371/journal.pone.0278225] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 11/14/2022] [Indexed: 01/18/2023] Open
Abstract
We introduced a brand-new member of the family that is going to be referred to as the New Power Topp-Leone Generated (NPTL-G). This new member is one of a kind. Given the major functions that created this new member, important mathematical aspects are discussed in as much detail as possible. We derived some functions for the new one, included the Rényi entropy, the qf, series development, and moment weighted probabilities. Moreover, to estimate the values of the parameters of our model that were not known, we employed the maximum likelihood technique. In addition, two actual datasets from the real world were investigated in order to bring attention to the possible applications of this novel distribution. This new model performs better than three key rivals based on the measurements that were collected.
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Affiliation(s)
- Mintodê Nicodème Atchadé
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Benin Republic
- University of Abomey-Calavi/International Chair in Mathematical Physics and Applications (ICMPA : UNESCO-Chair), Cotonou, Rep. Benin
- Department of Statistics and Econometrics, Saint-Petersburg State University of Economics, Saint-Petersburg, Russian Federation
- * E-mail:
| | - Melchior N’bouké
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Benin Republic
| | - Aliou Moussa Djibril
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Benin Republic
| | - Shabnam Shahzadi
- Department of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China
| | - Eslam Hussam
- Department of Mathmematics, Faculty of Science, Helwan University, Cairo, Egypt
| | - Ramy Aldallal
- Department of Accounting, College of Business Administration in Hawtat Bani Tamim, Prince Sattam Abdulaziz University, Al-Kharj, Saudi Arabia
| | - Huda M. Alshanbari
- Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
| | - Ahmed M. Gemeay
- Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
| | - Abdal-Aziz H. El-Bagoury
- Basic Science Department, Higher Institute of Engineering and Technology, El-Mahala El-Kobra, Egypt
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Almongy HM, Almetwally EM, Aljohani HM, Alghamdi AS, Hafez EH. A new extended rayleigh distribution with applications of COVID-19 data. RESULTS IN PHYSICS 2021; 23:104012. [PMID: 33728260 PMCID: PMC7952137 DOI: 10.1016/j.rinp.2021.104012] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Revised: 02/16/2021] [Accepted: 02/22/2021] [Indexed: 05/19/2023]
Abstract
This paper aims to model the COVID-19 mortality rates in Italy, Mexico, and the Netherlands, by specifying an optimal statistical model to analyze the mortality rate of COVID-19. A new lifetime distribution with three-parameter is introduced by a combination of Rayleigh distribution and extended odd Weibull family to produce the extended odd Weibull Rayleigh (EOWR) distribution. This new distribution has many excellent properties as simple linear representation, hazard rate function, and moment generating function. Maximum likelihood, maximum product spacing and Bayesian estimation methods are applied to estimate the unknown parameters of EOWR distribution. MCMC method is used for the Bayesian estimation. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. Also, data analysis for the real data of mortality rate is considered.
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Affiliation(s)
- Hisham M Almongy
- Department of Statistics, Faculty of Commerce, Mansoura University, Mansoura, Egypt
| | - Ehab M Almetwally
- Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Egypt
| | - Hassan M Aljohani
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
| | - Abdulaziz S Alghamdi
- Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia
| | - E H Hafez
- Mathematics Department, Faculty of Science, Helwan University, Helwan, Egypt
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EL-Helbawy AAA, AL-Dayian GR, Abd AL-Fattah AM. Statistical Inference for Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics. PAKISTAN JOURNAL OF STATISTICS AND OPERATION RESEARCH 2020:649-660. [DOI: 10.18187/pjsor.v16i4.2774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
In this paper, the shape parameters, reliability and hazard rate functions of the inverted Kumaraswamy distribution are estimated using maximum likelihood and Bayesian methods based on dual generalized order statistics. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on dual generalized order statistics. Confidence and credible intervals for the parameters, reliability and hazard rate functions are obtained. All results are specialized to lower record values, also a numerical study is presented to illustrate the theoretical procedures.
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Smith SE. The Hazard-Product method of generalization: Application to the gompertz and exponentiated Half-Normal distributions. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1425449] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Scott E. Smith
- University the Incarnate Word, BSH 206, University of the Incarnate Word, San Antonio, TX, USA
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