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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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Odhah OH, Alshanbari HM, Ahmad Z, Khan F, El-Bagoury AAAH. A new family of distributions using a trigonometric function: Properties and applications in the healthcare sector. Heliyon 2024; 10:e29861. [PMID: 38707268 PMCID: PMC11066639 DOI: 10.1016/j.heliyon.2024.e29861] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 04/07/2024] [Accepted: 04/16/2024] [Indexed: 05/07/2024] Open
Abstract
Probability distributions play a pivotal and significant role in modeling real-life data in every field. For this activity, a series of probability distributions have been introduced and exercised in applied sectors. This paper also contributes a new method for modeling continuous data sets. The proposed family is called the exponent power sine-G family of distributions. Based on the exponent power sine-G method, a new model, namely, the exponent power sine-Weibull model is studied. Several mathematical properties such as quantile function, identifiability property, and r t h moment are derived. For the exponent power sine-G method, the maximum likelihood estimators are obtained. Simulation studies are also presented. Finally, the optimality of the exponent power sine-Weibull model is shown by taking two applications from the healthcare sector. Based on seven evaluating criteria, it is demonstrated that the proposed model is the best competing distribution for analyzing healthcare phenomena.
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Affiliation(s)
- Omalsad Hamood Odhah
- Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
| | - Huda M. Alshanbari
- Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
| | - Zubair Ahmad
- Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan
| | - Faridoon Khan
- Pakistan Institute of Development Economics, Islamabad 44000, Pakistan
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3
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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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4
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Abd El Khaleq RH. The Generalized Odd Log-Logistic Fréchet Distribution for Modeling Extreme Values. PAKISTAN JOURNAL OF STATISTICS AND OPERATION RESEARCH 2022:649-674. [DOI: 10.18187/pjsor.v18i3.2902] [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
We introduce a new extension of the Fréchet distribution for modeling the extreme values. The new model generalizes eleven distributions at least, five of them are quite new. Some important mathematical properties of the new model are derived. We assess the performance of the maximum likelihood estimators (MLEs) via a simulation study. The new model is better than some other important competitive models in modeling the breaking stress data, the glass fibers data and the relief time data.
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Arshad M, Khetan M, Kumar V, Pathak AK. Record-based transmuted generalized linear exponential distribution with increasing, decreasing and bathtub shaped failure rates. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2106494] [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)
- Mohd Arshad
- Department of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, India
| | - Mukti Khetan
- Department of Mathematics, Amity University Mumbai, Maharashtra, India
| | - Vijay Kumar
- Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India
| | - Ashok Kumar Pathak
- Department of Mathematics and Statistics, Central University of Punjab, Bathinda, India
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6
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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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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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8
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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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9
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A New Wavelet-Based Privatization Mechanism for Probability Distributions. SENSORS 2022; 22:s22103743. [PMID: 35632152 PMCID: PMC9143979 DOI: 10.3390/s22103743] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 05/11/2022] [Accepted: 05/11/2022] [Indexed: 01/27/2023]
Abstract
In this paper, we propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the signal of a digital image sensor. Wavelets are employed to extract information from a wide range of types of data, including audio signals and images often related to sensors, as unstructured data. Specifically, the cumulative wavelet integral function is defined to build the perturbation on a probability with the help of this function. We show that an arbitrary distribution function additively perturbed is still a distribution function, which can be seen as a privatized distribution, with the privatization mechanism being a wavelet function. Thus, we offer a mathematical method for choosing a suitable probability distribution for data by starting from some guessed initial distribution. Examples of the proposed method are discussed. Computational experiments were carried out using a database-sensor and two related algorithms. Several knowledge areas can benefit from the new approach proposed in this investigation. The areas of artificial intelligence, machine learning, and deep learning constantly need techniques for data fitting, whose areas are closely related to sensors. Therefore, we believe that the proposed privatization mechanism is an important contribution to increasing the spectrum of existing techniques.
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10
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The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications. MATHEMATICS 2022. [DOI: 10.3390/math10091421] [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
Here, a new method is recommended to characterize a new continuous distribution class, named the generalized alpha exponent power family of distributions (GAEPFDs). A particular sub-model is presented for exemplifying the objective. The basic statistical properties, such as ordinary moments, the probability weighted moments, mode, quantile, order statistics, entropy measures, and moment generating functions, etc., were explored. To gauge the GAEPPRD parameters, the ML technique was utilized. The estimator behaviour was studied by a Monte Carlo simulation study (MCSS). The effectiveness of GAEPFDs was demonstrated observationally through lifetime data. The applications show that GAEPFDs can offer preferable results over other competitive models.
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11
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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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12
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Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2022:2739685. [PMID: 35047032 PMCID: PMC8763542 DOI: 10.1155/2022/2739685] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/14/2021] [Revised: 10/08/2021] [Accepted: 12/21/2021] [Indexed: 11/17/2022]
Abstract
Online marketing refers to the practices of promoting a company's brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company's product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.
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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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14
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Ramos PL, Louzada F. A note on the exponential geometric power series distribution. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2019.1634815] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Pedro Luiz Ramos
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil
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15
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Modeling Cancer Remission Time Data by Means of the Max Erlang Binomial Distribution. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2021; 2021:9932729. [PMID: 34608400 PMCID: PMC8487378 DOI: 10.1155/2021/9932729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Accepted: 08/21/2021] [Indexed: 11/18/2022]
Abstract
In this paper, a statistical simulation algorithm for the power series distribution, called the Max Erlang Binomial distribution, is proposed, analyzed, and tested for bladder cancer remission time data. In order to present the simulation technique, the EM algorithm for statistical estimation aimed at estimating the model parameters is described.
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16
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Bantan RAR, Chesneau C, Jamal F, Elbatal I, Elgarhy M. The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data. ENTROPY 2021; 23:e23081088. [PMID: 34441228 PMCID: PMC8391697 DOI: 10.3390/e23081088] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Revised: 08/17/2021] [Accepted: 08/19/2021] [Indexed: 11/16/2022]
Abstract
In this article, the "truncated-composed" scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.
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Affiliation(s)
- Rashad A. R. Bantan
- Department of Marine Geology, Faculty of Marine Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia;
| | - Christophe Chesneau
- Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
- Correspondence:
| | - Farrukh Jamal
- Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan;
| | - Ibrahim Elbatal
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia;
| | - Mohammed Elgarhy
- The Higher Institute of Commercial Sciences, Al mahalla Al kubra, Algarbia 31951, Egypt;
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17
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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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18
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A New Extended- X Family of Distributions: Properties and Applications. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2021; 2020:4650520. [PMID: 32549906 PMCID: PMC7270997 DOI: 10.1155/2020/4650520] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 01/21/2020] [Accepted: 04/29/2020] [Indexed: 11/17/2022]
Abstract
During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.
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19
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Catana LI, Preda V. Comparing the extremes order statistics between two random variables sequences using transmuted distributions. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1898641] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Luigi-Ionut Catana
- Faculty of Mathematics and Computer Science, Mathematical Doctoral School, University of Bucharest, Bucharest, Romania
| | - Vasile Preda
- Gheorghe Mihoc-Caius Iacob, Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania
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20
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The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science. Symmetry (Basel) 2021. [DOI: 10.3390/sym13030474] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.
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21
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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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22
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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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Abstract
The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has not been given special attention. This paper shows that the unit-Rayleigh distribution is much more interesting than it might at first glance, revealing closed-form expressions of important functions, and new desirable properties for application purposes. More precisely, on the theoretical level, we contribute to the following aspects: (i) we bring new characteristics on the form analysis of its main probabilistic and reliability functions, and show that the possible mode has a simple analytical expression, (ii) we prove new stochastic ordering results, (iii) we expose closed-form expressions of the incomplete and probability weighted moments at the basis of various probability functions and measures, (iv) we investigate distributional properties of the order statistics, (v) we show that the reliability coefficient can have a simple ratio expression, (vi) we provide a tractable expansion for the Tsallis entropy and (vii) we propose some bivariate unit-Rayleigh distributions. On a practical level, we show that the maximum likelihood estimate has a quite simple closed-form. Three data sets are analyzed and adjusted, revealing that the unit-Rayleigh distribution can be a better alternative to standard one-parameter unit distributions, such as the one-parameter Kumaraswamy, Topp–Leone, one-parameter beta, power and transmuted distributions.
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Ahmad Z, Mahmoudi E, Alizadeh M. Modelling insurance losses using a new beta power transformed family of distributions. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1743859] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Zubair Ahmad
- Department of Statistics, Yazd University, Yazd, Iran
| | - Eisa Mahmoudi
- Department of Statistics, Yazd University, Yazd, Iran
| | - Morad Alizadeh
- Department of Statistics, College of Science, Persian Gulf University, Bushehr, Iran
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Ahmad Z, Mahmoudi E, Hamedani GG, Kharazmi O. New methods to define heavy-tailed distributions with applications to insurance data. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1741942] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Zubair Ahmad
- Department of Statistics, Yazd University, Yazd, Iran
| | - Eisa Mahmoudi
- Department of Statistics, Yazd University, Yazd, Iran
| | - G. G. Hamedani
- Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI, USA
| | - Omid Kharazmi
- Department of Statistics, Faculty of Sciences, Vali-e-Asr university of Rafsanjan, Rafsanjan, Iran
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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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A Flexible Reduced Logarithmic- X Family of Distributions with Biomedical Analysis. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2020; 2020:4373595. [PMID: 32148556 PMCID: PMC7053460 DOI: 10.1155/2020/4373595] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2019] [Revised: 01/19/2020] [Accepted: 01/20/2020] [Indexed: 11/17/2022]
Abstract
Statistical distributions play a prominent role in applied sciences, particularly in biomedical sciences. The medical data sets are generally skewed to the right, and skewed distributions can be used quite effectively to model such data sets. In the present study, therefore, we propose a new family of distributions to model right skewed medical data sets. The proposed family may be named as a flexible reduced logarithmic-X family. The proposed family can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. A special submodel of the proposed family called, a flexible reduced logarithmic-Weibull distribution, is discussed in detail. Some mathematical properties of the proposed family and certain related characterization results are presented. The maximum likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is done to evaluate the performance of these estimators. Finally, for the illustrative purposes, three applications from biomedical sciences are analyzed and the goodness of fit of the proposed distribution is compared to some well-known competitors.
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Abstract
In this paper, we introduce a new general family of distributions obtained by a subtle combination of two well-established families of distributions: the so-called power Topp–Leone-G and inverse exponential-G families. Its definition is centered around an original cumulative distribution function involving exponential and polynomial functions. Some desirable theoretical properties of the new family are discussed in full generality, with comprehensive results on stochastic ordering, quantile function and related measures, general moments and related measures, and the Shannon entropy. Then, a statistical parametric model is constructed from a special member of the family, defined with the use of the inverse Lomax distribution as the baseline distribution. The maximum likelihood method was applied to estimate the unknown model parameters. From the general theory of this method, the asymptotic confidence intervals of these parameters were deduced. A simulation study was conducted to evaluate the numerical behavior of the estimates we obtained. Finally, in order to highlight the practical perspectives of the new family, two real-life data sets were analyzed. All the measures considered are favorable to the new model in comparison to four serious competitors.
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Ramos PL, Dey DK, Louzada F, Lachos VH. An extended poisson family of life distribution: a unified approach in competitive and complementary risks. J Appl Stat 2019; 47:306-322. [PMID: 35706514 DOI: 10.1080/02664763.2019.1644488] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
In this paper, we introduce a new approach to generate flexible parametric families of distributions. These models arise on competitive and complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum/maximum lifetime value among all risks. The latent variables have a zero-truncated Poisson distribution. For the proposed family of distribution, the extra shape parameter has an important physical interpretation in the competing and complementary risks scenario. The mathematical properties and inferential procedures are discussed. The proposed approach is applied in some existing distributions in which it is fully illustrated by an important data set.
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Affiliation(s)
- Pedro L Ramos
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil.,Department of Statistics, University of Connecticut, Storrs, CT, USA
| | - Dipak K Dey
- Department of Statistics, University of Connecticut, Storrs, CT, USA
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil
| | - Victor H Lachos
- Department of Statistics, University of Connecticut, Storrs, CT, USA
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Abstract
A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.
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Abstract
In this paper, we study a new four-parameter distribution called the odd gamma Weibull-geometric distribution. Having the qualities suggested by its name, the new distribution is a special member of the odd-gamma-G family of distributions, defined with the Weibull-geometric distribution as baseline, benefiting of their respective merits. Firstly, we present a comprehensive account of its mathematical properties, including shapes, asymptotes, quantile function, quantile density function, skewness, kurtosis, moments, moment generating function and stochastic ordering. Then, we focus our attention on the statistical inference of the corresponding model. The maximum likelihood estimation method is used to estimate the model parameters. The performance of this method is assessed by a Monte Carlo simulation study. An empirical illustration of the new distribution is presented by the analyses two real-life data sets. The results of the proposed model reveal to be better as compared to those of the useful beta-Weibull, gamma-Weibull and Weibull-geometric models.
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Granzotto DCT, Ferreira PH, Louzada F. Likelihood-based inference for the transmuted log-logistic model in the presence of right-censored data. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1440313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
| | - Paulo H. Ferreira
- Department of Statistics, Federal University of Bahia, Salvador, Bahia, Brazil
| | - Francisco Louzada
- Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos, São Paulo, Brazil
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Chesneau C, Bakouch HS, Hussain T. A new class of probability distributions via cosine and sine functions with applications. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1440303] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
| | - Hassan S. Bakouch
- Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
| | - Tassaddaq Hussain
- Mirpur University of Science and Technology (MUST), Mirpur, (AJK), Pakistan
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Chhetri SB, Akinsete AA, Aryal G, Long H. The Kumaraswamy transmuted Pareto distribution. JOURNAL OF STATISTICAL DISTRIBUTIONS AND APPLICATIONS 2017. [DOI: 10.1186/s40488-017-0065-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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