1
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Imran M, Alsadat N, Tahir MH, Jamal F, Elgarhy M, Ahmad H, Johannssen A. The development of an extended Weibull model with applications to medicine, industry and actuarial sciences. Sci Rep 2024; 14:12338. [PMID: 38811667 PMCID: PMC11190291 DOI: 10.1038/s41598-024-61308-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Accepted: 05/03/2024] [Indexed: 05/31/2024] Open
Abstract
This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.
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Affiliation(s)
- Muhammad Imran
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
| | - Najwan Alsadat
- Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, 11587, Riyadh, Saudi Arabia
| | - M H Tahir
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
| | - Farrukh Jamal
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan
| | - Mohammed Elgarhy
- Department of Basic Sciences, Higher Institute for Administrative Sciences, Belbeis, Al-Sharqia, Egypt
- Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62521, Egypt
| | - Hijaz Ahmad
- Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
- Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Arne Johannssen
- Faculty of Business Administration, University of Hamburg, 20146, Hamburg, Germany.
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2
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Jamal F, Alqawba M, Altayab Y, Iqbal T, Afify AZ. A unified exponential-H family for modeling real-life data: Properties and inference. Heliyon 2024; 10:e27661. [PMID: 38509929 PMCID: PMC10951600 DOI: 10.1016/j.heliyon.2024.e27661] [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: 07/05/2023] [Revised: 02/28/2024] [Accepted: 03/05/2024] [Indexed: 03/22/2024] Open
Abstract
The exponential distribution is one of the most widely used statistical distribution for reliability issues. In this paper, we introduce a novel family based on the exponential model, called the new exponential-H (NEx-H) family. The sub-models of the NEx-H family are capable of accommodating variable failure rates, as well as unimodal, bimodal, left-skewed, symmetric, right-skewed, and J-shape densities. The mathematical features of the NEx-H family are derived. The parameters of the NEx-Weibull distribution are estimated by using seven estimation methods. Detailed numerical simulations are presented. Based on our study, the maximum likelihood is the best estimation method for estimating the NEx-Weibull parameters. Three real-life data sets are fitted using the NEx-Weibull distribution. The NEx-Weibull model provides better fit as compared to some competing Weibull models.
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Affiliation(s)
- Farrukh Jamal
- Department of Statistics, The Islamia University Bahawalpur, 63100, Pakistan
| | - Mohammed Alqawba
- Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
| | - Yasser Altayab
- Department of Management, College of Business Administration, University of Khorfakkan, P.O. Box: 18119, Khorfakkan, United Arab Emirates
| | - Tariq Iqbal
- Govt. Makhdoom Shams-ud-Din Gillani Associate College Uch Sharif, Ahmad Pur East, Pakistan
| | - Ahmed Z. Afify
- Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
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3
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Karakaya K, Rajitha CS, Sağlam Ş, Tashkandy YA, Bakr ME, Muse AH, Kumar A, Hussam E, Gemeay AM. A new unit distribution: properties, estimation, and regression analysis. Sci Rep 2024; 14:7214. [PMID: 38532007 DOI: 10.1038/s41598-024-57390-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 03/18/2024] [Indexed: 03/28/2024] Open
Abstract
This research commences a unit statistical model named power new power function distribution, exhibiting a thorough analysis of its complementary properties. We investigate the advantages of the new model, and some fundamental distributional properties are derived. The study aims to improve insight and application by presenting quantitative and qualitative perceptions. To estimate the three unknown parameters of the model, we carefully examine various methods: the maximum likelihood, least squares, weighted least squares, Anderson-Darling, and Cramér-von Mises. Through a Monte Carlo simulation experiment, we quantitatively evaluate the effectiveness of these estimation methods, extending a robust evaluation framework. A unique part of this research lies in developing a novel regressive analysis based on the proposed distribution. The application of this analysis reveals new viewpoints and improves the benefit of the model in practical situations. As the emphasis of the study is primarily on practical applications, the viability of the proposed model is assessed through the analysis of real datasets sourced from diverse fields.
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Affiliation(s)
- Kadir Karakaya
- Department of Statistics, Faculty of Sciences, Selcuk University, Konya, Turkey
| | - C S Rajitha
- Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India
| | - Şule Sağlam
- Department of Statistics, Faculty of Sciences, Selcuk University, Konya, Turkey
| | - Yusra A Tashkandy
- Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
| | - M E Bakr
- Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
| | - Abdisalam Hassan Muse
- Faculty of Science and Humanities, School of Postgraduate Studies and Research (SPGSR), Amoud University, Borama, Somalia.
| | - Anoop Kumar
- Department of Statistics, Faculty of Basic Science, Central University of Haryana, Mahendergarh, 123031, India
| | - Eslam Hussam
- Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
| | - Ahmed M Gemeay
- Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt
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4
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Peña-Ramírez FA, Guerra RR, Mafalda CP. The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. PLoS One 2023; 18:e0290885. [PMID: 37972044 PMCID: PMC10653530 DOI: 10.1371/journal.pone.0290885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 08/11/2023] [Indexed: 11/19/2023] Open
Abstract
We propose a new family of distributions, so-called the unit ratio-extended Weibull family ([Formula: see text]). It is derived from ratio transformation in an extended Weibull random variable. The use of this transformation is a novelty of the work since it has been less explored than the exponential and has not yet been studied within the extended Weibull class. Moreover, we offer a valuable alternative to model double-bounded variables on the unit interval. Five [Formula: see text] special models are studied in detail, namely the: i) unit ratio-Gompertz; ii) unit ratio-Burr XII; iii) unit ratio-Lomax; v) unit ratio-Rayleigh, and vi) unit ratio-Weibull distributions. We propose a quantile-parameterization for the new family. The maximum likelihood estimators (MLEs) are presented. A Monte Carlo study is performed to evaluate the behavior of the MLEs of unit ratio-Gompertz and unit ratio-Rayleigh distributions. This last model has closed-form and approximately unbiased MLE for small sample sizes. Further, the [Formula: see text] submodels are adjusted to the dropout rate in Brazilian undergraduate courses. We focus on the areas of civil engineering, economics, computer sciences, and control engineering. The applications show that the new family is suitable for modeling educational data and may provide effective alternatives compared to other usual unit models, such as the Beta, Kumaraswamy, and unit gamma distributions. They can also outperform some recent contributions in the unit distribution literature. Thus, the [Formula: see text] family can provide competitive alternatives when those models are unsuitable.
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Affiliation(s)
| | - Renata R. Guerra
- Departamento de Estatística, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil
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5
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Alnssyan B, Hussein EA, Alizadeh M, Afify AZ, Abdellatif AD. The weighted Lindley-G family of probabilistic models: properties, inference, and applications to real-life data. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2023. [DOI: 10.3233/jifs-222758] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/26/2023]
Abstract
We propose a new wider family called the weighted Lindley-G family. We derive some mathematical properties and special sub-models of the new family. We address the estimation of the model parameters by eight approaches of estimation. The estimation approaches are ranked and compared by using detailed simulations to develop a guideline for choosing the best approach for estimating the distribution parameters. The potentiality of the new family is illustrated via two applications to real-life data. It is shown that the proposed WLi-G family is more flexible as compared to some of the most cited families in the distribution theory literature such as the exponentiated-G, beta-G, transmuted-G, and alpha-power-G families under the same baseline model.
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Affiliation(s)
- Badr Alnssyan
- Unit of Scientific Research, Applied College, Qassim University, Buraydah, Saudi Arabia
| | | | - Morad Alizadeh
- Department of Statistics, Persian Gulf University, Bushehr, Iran
| | - Ahmed Z. Afify
- Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt
| | - Ashraf D. Abdellatif
- Department of Technological Management and Information, Higher Technological Institute, 10th of Ramadan, Egypt
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6
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Cordeiro GM, Vasconcelos JCS, dos Santos DP, Ortega EMM, Sermarini RA. Three mixed-effects regression models using an extended Weibull with applications on games in differential and integral calculus. BRAZ J PROBAB STAT 2022. [DOI: 10.1214/22-bjps553] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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7
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Reis LDR, Cordeiro GM, Lima MDCS. The unit gamma-G class: properties, simulations, regression and applications. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2112601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Lucas David R. Reis
- Department of Statistics, Federal University of Pernambuco, Recife, Pernambuco, Brazil
| | - Gauss M. Cordeiro
- Department of Statistics, Federal University of Pernambuco, Recife, Pernambuco, Brazil
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Cordeiro GM, Vasconcelos JCS, Ortega EMM, Marinho PRD. A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications. AN ACAD BRAS CIENC 2022; 94:e20201972. [PMID: 35857939 DOI: 10.1590/0001-3765202220201972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 06/07/2021] [Indexed: 11/21/2022] Open
Abstract
We define two new flexible families of continuous distributions to fit real data by compoun-ding the Marshall-Olkin class and the power series distribution. These families are very competitive to the popular beta and Kumaraswamy generators. Their densities have linear representations of exponentiated densities. In fact, as the main properties of thirty five exponentiated distributions are well-known, we can easily obtain several properties of about three hundred fifty distributions using the references of this article and five special cases of the power series distribution. We provide a package implemented in R software that shows numerically the precision of one of the linear representations. This package is useful to calculate numerical values for some statistical measurements of the generated distributions. We estimate the parameters by maximum likelihood. We define a regression based on one of the two families. The usefulness of a generated distribution and the associated regression is proved empirically.
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Affiliation(s)
- Gauss M Cordeiro
- Universidade Federal de Pernambuco, Departamento de Estatística, Avenida Professor Moraes Rego, s/n, Bairro Iputinga, 50670-901 Recife, PE, Brazil
| | - Julio Cezar S Vasconcelos
- Universidade de São Paulo, Departamento de Ciências Exatas, Avenida Pádua Dias, 11, Bairro São Dimas, 13418-900 Piracicaba, SP, Brazil
| | - Edwin M M Ortega
- Universidade de São Paulo, Departamento de Ciências Exatas, Avenida Pádua Dias, 11, Bairro São Dimas, 13418-900 Piracicaba, SP, Brazil
| | - Pedro Rafael D Marinho
- Universidade Federal da Paraíba, Departamento de Estatística, Cidade Universitária, s/n, Bairro Castelo Branco, 58054-900 João Pessoa, PB, Brazil
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9
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A New Useful Exponential Model with Applications to Quality Control and Actuarial Data. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2022:2489998. [PMID: 35720884 PMCID: PMC9203186 DOI: 10.1155/2022/2489998] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 05/10/2022] [Indexed: 12/02/2022]
Abstract
The compounding approach is used to introduce a new family of distributions called exponentiated Bell G, analogy to exponentiated G Poisson. Several essential properties of the proposed family are obtained. The special model called exponentiated Bell exponential (EBellE) is presented along with properties. Furthermore, the risk theory related measures including value-at-risk and expected-shortfall are also computed for the special model. Group acceptance sampling plan is designed when a lifetime of a product or item follows an EBellE model taking median as a quality parameter. The parameters of the proposed model are estimated by considering maximum likelihood approach along with simulation analysis. The usefulness of the proposed model is illustrated by practical means which yield better fits as compared to several exponential related extended models.
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10
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Bakr ME, Al-Babtain AA, Mahmood Z, Aldallal RA, Khosa SK, El-Raouf MMA, Hussam E, Gemeay AM. Statistical modelling for a new family of generalized distributions with real data applications. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:8705-8740. [PMID: 35942732 DOI: 10.3934/mbe.2022404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
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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Affiliation(s)
- M E Bakr
- Department of Statistics and Operation Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
| | - Abdulhakim A Al-Babtain
- Department of Statistics and Operation Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
| | - Zafar Mahmood
- Government Associate College, Khairpur Tamewali, Bahawalpur, Pakistan
| | - R A Aldallal
- College of Business Administration in Hotat bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
| | - Saima Khan Khosa
- Department of Mathematics and Statistics University of Saskatchewan, Saskatoon, SK, Canada
| | - M M Abd El-Raouf
- Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Alexandria, Egypt
| | - Eslam Hussam
- Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
| | - Ahmed M Gemeay
- Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
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11
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Dhungana GP, Kumar V. Exponentiated Odd Lomax Exponential distribution with application to COVID-19 death cases of Nepal. PLoS One 2022; 17:e0269450. [PMID: 35657989 PMCID: PMC9165905 DOI: 10.1371/journal.pone.0269450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 05/21/2022] [Indexed: 11/18/2022] Open
Abstract
This study suggested a new four-parameter Exponentiated Odd Lomax Exponential (EOLE) distribution by compounding an exponentiated odd function with Lomax distribution as a generator. The proposed model is unimodal and positively skewed whereas the hazard rate function is monotonically increasing and inverted bathtubs. Some important properties of the new distribution are derived such as quintile function and median; asymptotic properties and mode; moments; mean residual life, mean path time; mean deviation; order statistics; and Bonferroni & Lorenz curve. The value of the parameters is obtained from the maximum likelihood estimation, least-square estimation, and Cramér-Von-Mises methods. Here, a simulation study and two real data sets, “the number of deaths per day due to COVID-19 of the first wave in Nepal" and ‘‘failure stresses (In Gpa) of single carbon fibers of lengths 50 mm", have been applied to validate the different theoretical findings. The finding of an order of COVID-19 deaths in 153 days in Nepal obey the proposed distribution, it has a significantly positive relationship between the predictive test positive rate and the predictive number of deaths per day. Therefore, the intended model is an alternative model for survival data and lifetime data analysis.
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Affiliation(s)
- Govinda Prasad Dhungana
- Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India
- Department of Statistics, Tribhuvan University, Birendra Multiple Campus, Bharatpur, Nepal
- * E-mail: ,
| | - Vijay Kumar
- Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India
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A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right-Censored Healthcare Data. JOURNAL OF HEALTHCARE ENGINEERING 2022; 2022:2051642. [PMID: 35693888 PMCID: PMC9184216 DOI: 10.1155/2022/2051642] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Revised: 03/24/2022] [Accepted: 04/18/2022] [Indexed: 11/17/2022]
Abstract
Survival analysis is a collection of statistical techniques which examine the time it takes for an event to occur, and it is one of the most important fields in biomedical sciences and other variety of scientific disciplines. Furthermore, the computational rapid advancements in recent decades have advocated the application of Bayesian techniques in this field, giving a powerful and flexible alternative to the classical inference. The aim of this study is to consider the Bayesian inference for the generalized log-logistic proportional hazard model with applications to right-censored healthcare data sets. We assume an independent gamma prior for the baseline hazard parameters and a normal prior is placed on the regression coefficients. We then obtain the exact form of the joint posterior distribution of the regression coefficients and distributional parameters. The Bayesian estimates of the parameters of the proposed model are obtained using the Markov chain Monte Carlo (McMC) simulation technique. All computations are performed in Bayesian analysis using Gibbs sampling (BUGS) syntax that can be run with Just Another Gibbs Sampling (JAGS) from the R software. A detailed simulation study was used to assess the performance of the proposed parametric proportional hazard model. Two real-survival data problems in the healthcare are analyzed for illustration of the proposed model and for model comparison. Furthermore, the convergence diagnostic tests are presented and analyzed. Finally, our research found that the proposed parametric proportional hazard model performs well and could be beneficial in analyzing various types of survival data.
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Fayomi A, Khan S, Tahir MH, Algarni A, Jamal F, Abu-Shanab R. A new extended gumbel distribution: Properties and application. PLoS One 2022; 17:e0267142. [PMID: 35622822 PMCID: PMC9140309 DOI: 10.1371/journal.pone.0267142] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 04/01/2022] [Indexed: 11/18/2022] Open
Abstract
A robust generalisation of the Gumbel distribution is proposed in this article. This family of distributions is based on the T-X paradigm. From a list of special distributions that have evolved as a result of this family, three separate models are also mentioned in this article. A linear combination of generalised exponential distributions can be used to characterise the density of a new family, which is critical in assessing some of the family’s properties. The statistical features of this family are determined, including exact formulations for the quantile function, ordinary and incomplete moments, generating function, and order statistics. The model parameters are estimated using the maximum likelihood method. Further, one of the unique models has been systematically studied. Along with conventional skewness measures, MacGillivray skewness is also used to quantify the skewness measure. The new probability distribution also enables us to determine certain critical risk indicators, both numerically and graphically. We use a simulated assessment of the suggested distribution, as well as apply three real-world data sets in modelling the proposed model, in order to ensure its authenticity and superiority.
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Affiliation(s)
- Aisha Fayomi
- Faculty of Science, Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia
| | - Sadaf Khan
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
- * E-mail:
| | | | - Ali Algarni
- Faculty of Science, Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia
| | - Farrukh Jamal
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
| | - Reman Abu-Shanab
- Department of Mathematics, College of Science, University of Bahrain, Zallaq, Bahrain
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14
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A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1). Symmetry (Basel) 2022. [DOI: 10.3390/sym14051040] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model.
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Classical and Bayesian Inference on Finite Mixture of Exponentiated Kumaraswamy Gompertz and Exponentiated Kumaraswamy Fréchet Distributions under Progressive Type II Censoring with Applications. MATHEMATICS 2022. [DOI: 10.3390/math10091496] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
A finite mixture of exponentiated Kumaraswamy Gompertz and exponentiated Kumaraswamy Fréchet is developed and discussed as a novel probability model. We study some useful structural properties of the proposed model. To estimate the model parameters under the classical method, we use the maximum likelihood estimation using a progressive type II censoring scheme. Under the Bayesian paradigm the estimation is carried out with gamma priors under a progressive type II censored samples with squared error loss function. To demonstrate the efficiency of the proposed model based on progressively type II censoring, a simulation study is carried out. Three actual data sets are used as an example, demonstrating that the suggested model in the new class fits better than the existing finite mixture models available in the literature.
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A Modified Power Family of Distributions: Properties, Simulations and Applications. MATHEMATICS 2022. [DOI: 10.3390/math10071035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, we present a new class of distributions called the modified power family by adding an extra shape parameter. Some of its structural properties are derived. Three special cases of the new family are considered and estimated using the method of maximum likelihood. The validity of the method of maximum likelihood is illustrated via Monte Carlo simulations. The importance and flexibility of the new family are empirically illustrated, partly due to efficient modeling of several real data. We compare the proposed family with some distributions and special models generated from other classes using classical statistical measures.
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17
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The Minimum Lindley Lomax Distribution: Properties and Applications. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2022. [DOI: 10.3390/mca27010016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
By fusing the Lindley and Lomax distributions, we present a unique three-parameter continuous model titled the minimum Lindley Lomax distribution. The quantile function, ordinary and incomplete moments, moment generating function, Lorenz and Bonferroni curves, order statistics, Rényi entropy, stress strength model, and stochastic sequencing are all carefully examined as basic statistical aspects of the new distribution. The characterizations of the new model are investigated. The proposed distribution’s parameters were evaluated using the maximum likelihood procedures. The stability of the parameter estimations is explored using a Monte Carlo simulation. Two applications are used to objectively assess the new model’s extensibility.
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Abstract
We introduce a new flexible modified alpha power (MAP) family of distributions by adding two parameters to a baseline model. Some of its mathematical properties are addressed. We show empirically that the new family is a good competitor to the Beta-F and Kumaraswamy-F classes, which have been widely applied in several areas. A new extension of the exponential distribution, called the modified alpha power exponential (MAPE) distribution, is defined by applying the MAP transformation to the exponential distribution. Some properties and maximum likelihood estimates are provided for this distribution. We analyze three real datasets to compare the flexibility of the MAPE distribution to the exponential, Weibull, Marshall–Olkin exponential and alpha power exponential distributions.
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Kharazmi O, Hamedani GG, Cordeiro GM. Log-mean distribution: applications to medical data, survival regression, Bayesian and non-Bayesian discussion with MCMC algorithm. J Appl Stat 2022; 50:1152-1177. [PMID: 37009595 PMCID: PMC10062237 DOI: 10.1080/02664763.2021.2023117] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
We introduce a new family via the log mean of an underlying distribution and as baseline the proportional hazards model and derive some important properties. A special model is proposed by taking the Weibull for the baseline. We derive several properties of the sub-model such as moments, order statistics, hazard function, survival regression and certain characterization results. We estimate the parameters using frequentist and Bayesian approaches. Further, Bayes estimators, posterior risks, credible intervals and highest posterior density intervals are obtained under different symmetric and asymmetric loss functions. A Monte Carlo simulation study examines the biases and mean square errors of the maximum likelihood estimators. For the illustrative purposes, we consider heart transplant and bladder cancer data sets and investigate the efficiency of proposed model.
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Affiliation(s)
- O. Kharazmi
- Department of Statistics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
| | - G. G. Hamedani
- Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI, USA
| | - G. M. Cordeiro
- Department of Statistics, Universidade Federal de Pernambuco, Recife, Brazil
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20
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PINHO LUISG, NOBRE JUVÊNCIOS, CORDEIRO GAUSSM. Continuous Probability Distributions generated by the PIPE Algorithm. AN ACAD BRAS CIENC 2022; 94:e20201542. [DOI: 10.1590/0001-3765202220201542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 11/04/2021] [Indexed: 11/09/2022] Open
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21
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Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2021; 2021:8640794. [PMID: 34782836 PMCID: PMC8590594 DOI: 10.1155/2021/8640794] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Accepted: 10/05/2021] [Indexed: 11/18/2022]
Abstract
The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall-Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.
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22
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An Alternate Generalized Odd Generalized Exponential Family with Applications to Premium Data. Symmetry (Basel) 2021. [DOI: 10.3390/sym13112064] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family’s properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, Rényi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family’s parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fréchet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.
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23
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On the Discrete Weibull Marshall–Olkin Family of Distributions: Properties, Characterizations, and Applications. AXIOMS 2021. [DOI: 10.3390/axioms10040287] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, we introduce a new flexible discrete family of distributions, which accommodates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets.
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24
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Goyal T, Maurya SK, Nadarajah S. Geometric generated family of distributions: A review. BRAZ J PROBAB STAT 2021. [DOI: 10.1214/20-bjps485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Teena Goyal
- Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan, India
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25
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Group Acceptance Sampling Plan Using Marshall–Olkin Kumaraswamy Exponential (MOKw-E) Distribution. Processes (Basel) 2021. [DOI: 10.3390/pr9061066] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The current research concerns the group acceptance sampling plan in the case where (i) the lifetime of the items follows the Marshall–Olkin Kumaraswamy exponential distribution (MOKw-E) and (ii) a large number of items, considered as a group, can be tested at the same time. When the consumer’s risk and the test terminsation period are defined, the key design parameters are extracted. The values of the operating characteristic function are determined for different quality levels. At the specified producer’s risk, the minimum ratios of the true average life to the specified average life are also calculated. The results of the present study will set the platform for future research on various nano quality level topics when the items follow different probability distributions under the Marshall–Olkin Kumaraswamy scheme. Real-world data are used to explain the technique.
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26
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Tahir MH, Hussain MA, Cordeiro GM. A new flexible generalized family for constructing many families of distributions. J Appl Stat 2021; 49:1615-1635. [DOI: 10.1080/02664763.2021.1874891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- M. H. Tahir
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
| | - M. Adnan Hussain
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
| | - Gauss M. Cordeiro
- Department of Statistics, Federal University of Pernambuco, Recife, Brazil
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27
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A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension. MATHEMATICS 2020. [DOI: 10.3390/math8111989] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.
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29
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Peña-Ramírez FA, Guerra RR, Cordeiro GM, Marinho PRD. The Exponentiated Power Generalized Weibull: Properties and Applications. AN ACAD BRAS CIENC 2020; 90:2553-2577. [PMID: 30304207 DOI: 10.1590/0001-3765201820170423] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Accepted: 11/01/2017] [Indexed: 11/22/2022] Open
Abstract
We propose a new lifetime model called the exponentiated power generalized Weibull (EPGW) distribution, which is obtained from the exponentiated family applied to the power generalized Weibull (PGW) distribution. It can also be derived from a power transform on an exponentiated Nadarajah-Haghighi random variable. Since several structural properties of the PGW distribution have not been studied, they can be obtained from those of the EPGW distribution. The model is very flexible for modeling all common types of hazard rate functions. It is a very competitive model to the well-known Weibull, exponentiated exponential and exponentiated Weibull distributions, among others. We also give a physical motivation for the new distribution if the power parameter is an integer. Some of its mathematical properties are investigated. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters.
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Affiliation(s)
- Fernando A Peña-Ramírez
- Departamento de Estatística, Universidade Federal de Santa Maria, Cidade Universitária, Av. Roraima, 1000, 97105-900 Santa Maria, RS, Brazil
| | - Renata R Guerra
- Departamento de Estatística, Universidade Federal de Santa Maria, Cidade Universitária, Av. Roraima, 1000, 97105-900 Santa Maria, RS, Brazil
| | - Gauss M Cordeiro
- Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária,Av. Prof. Moraes Rego, 1235, 50740-540 Recife, PE, Brazil
| | - Pedro R D Marinho
- Departamento de Estatística, Universidade Federal da Paraíba, Cidade Universitária,Conj. Pres. Castelo Branco III, s/n, 58051-900 João Pessoa, PB, Brazil
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30
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Eliwa MS, El-Morshedy M. Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1741919] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- M. S. Eliwa
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
| | - M. El-Morshedy
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- Department of Mathematics, College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
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31
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SILVA RENILMAPDA, CYSNEIROS AUDREYHELENM, CORDEIRO GAUSSM, TABLADA CLAUDIOJAVIER. The Transmuted Marshall-Olkin Extended Lomax Distribution. AN ACAD BRAS CIENC 2020; 92:e20180777. [DOI: 10.1590/0001-3765202020180777] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Accepted: 01/12/2019] [Indexed: 11/21/2022] Open
Affiliation(s)
- RENILMA P. DA SILVA
- Universidade Federal de Pernambuco, Brazil; Universidade Federal de Rio Grande do Norte, Brazil
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32
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Abstract
In this paper, we propose a novel class of probability distributions called Normal-G. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifiability whenever the baseline is identifiable. We present special Normal-G sub-models, which can fit asymmetrical data with either positive or negative skew. Other important mathematical properties are described, such as the series expansion of the probability density function (pdf), which is used to derive expressions for the moments and the moment generating function (mgf). We bring Monte Carlo simulation studies to investigate the behavior of the maximum likelihood estimates (MLEs) of two distributions generated by the class and we also present applications to real datasets to illustrate its usefulness.
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33
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Haq MAU, Elgarhy M, Hashmi S. The generalized odd Burr III family of distributions: properties, applications and characterizations. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2019. [DOI: 10.1080/16583655.2019.1666785] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Muhammad Ahsan ul Haq
- College of Statistical & Actuarial Sciences, University of the Punjab, Lahore, Pakistan
- Quality Enhancement Cell, National College of Arts, Lahore, Pakistan
| | - M. Elgarhy
- Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia, Egypt
| | - Sharqa Hashmi
- Department of statistics, Lahore College of Women University (LCWU), Lahore, Pakistan
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34
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Silva R, Gomes-Silva F, Ramos M, Cordeiro GM, Marinho P, Andrade T. The Exponentiated Kumaraswamy-G Class: General Properties and Application. REVISTA COLOMBIANA DE ESTADÍSTICA 2019. [DOI: 10.15446/rce.v42n1.66205] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Abstract
We propose a new family of distributions called the exponentiated Kumaraswamy-G class with three extra positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive some mathematical properties of the proposed class including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean deviations, reliability, Rényi entropy and Shannon entropy. The method of maximum likelihood is used to fit the distributions in the proposed class. Simulations are performed in order to assess the asymptotic behavior of the maximum likelihood estimates. We illustrate its potentiality with applications to two real data sets which show that the extended Weibull model in the new class provides a better fit than other generalized Weibull distributions.
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35
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Affiliation(s)
- K. Jayakumar
- Department of Statistics, University of Calicut, Kerala, India
| | - K. K. Sankaran
- Department of Statistics, University of Calicut, Kerala, India
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36
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37
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Cordeiro GM, Bourguignon M, Ortega EMM, Ramires TG. General mathematical properties, regression and applications of the log-gamma-generated family. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2017.1316403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Gauss M. Cordeiro
- Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil
| | - Marcelo Bourguignon
- Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil
| | - Edwin M. M. Ortega
- Departamento de Estatística, Universidade de São Paulo, Piracicaba, Piracicaba, SP, Brazil
| | - Thiago G. Ramires
- Departamento de Estatística, Universidade de São Paulo, Piracicaba, Piracicaba, SP, Brazil
- Departamento de Matemática, Universidade Tecnológica Federal do Paraná, Apucarana, PR, Brazil
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38
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Matheson M, Muñoz A, Cox C. Describing the Flexibility of the Generalized Gamma and Related Distributions. JOURNAL OF STATISTICAL DISTRIBUTIONS AND APPLICATIONS 2017. [DOI: 10.1186/s40488-017-0072-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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39
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Matheson MB, Cox C. The shape of the hazard function: Does the generalized gamma have the last word? COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1277757] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Matthew B. Matheson
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
| | - Christopher Cox
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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40
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Tahir MH, Cordeiro GM. Compounding of distributions: a survey and new generalized classes. JOURNAL OF STATISTICAL DISTRIBUTIONS AND APPLICATIONS 2016. [DOI: 10.1186/s40488-016-0052-1] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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