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Hussain Z, Jamal F, Saboor A, Shafiq S, Khan A, Perveen S, Awwad FA, Ismail EA, Ali M. A novel two-parameter unit probability model with properties and applications. Heliyon 2024; 10:e37242. [PMID: 39309821 PMCID: PMC11414500 DOI: 10.1016/j.heliyon.2024.e37242] [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: 01/07/2024] [Revised: 08/29/2024] [Accepted: 08/29/2024] [Indexed: 09/25/2024] Open
Abstract
This paper develops a novel two-parameter unit probability model which is the generalized form Kumaraswami distribution that exhibits greater flexibility compared to well-known existing distributions, attributed to its distinct hazard and density function shapes. Extensive analysis has been conducted to explore numerous statistical features of the specified distribution, specifically moments, and order statistics providing explicit expressions for these measures. The maximum likelihood estimation is employed to estimate the model parameters and a numerical simulation analysis confirms the consistency of this estimation approach. Furthermore, the applicability of the specified model is demonstrated by considering four real data sets, showcasing its effectiveness in capturing the characteristics of real life data. The proposed model shows promise as a versatile tool for analyzing diverse data sets in a wide range of fields.
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Affiliation(s)
- Zawar Hussain
- Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
| | - Farrukh Jamal
- Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
| | - Abdus Saboor
- Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat, KP, 26000, Pakistan
| | - Shakaiba Shafiq
- Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
| | - Arshid Khan
- Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat, KP, 26000, Pakistan
| | - Shahida Perveen
- Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat, KP, 26000, Pakistan
| | - Fuad A. Awwad
- Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
| | - Emad A.A. Ismail
- Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
| | - Musharraf Ali
- Department of Mathematics, G.F. College, Shahjahanpur, Affiliated M.J.P. Rohilkhand University, Bareilly, India
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Alotaibi N, Al-Moisheer A, Hassan AS, Elbatal I, Alyami SA, Almetwally EM. Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring. Heliyon 2024; 10:e36774. [PMID: 39315172 PMCID: PMC11417215 DOI: 10.1016/j.heliyon.2024.e36774] [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: 04/24/2024] [Revised: 08/21/2024] [Accepted: 08/22/2024] [Indexed: 09/25/2024] Open
Abstract
This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.
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Affiliation(s)
- Naif Alotaibi
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
| | - A.S. Al-Moisheer
- Department of Mathematics, College of Science, Jouf University, P.O. Box 848, Sakaka, 72351, Saudi Arabia
| | - Amal S. Hassan
- Faculty of Graduate Studies for Statistical Research, Cairo University, 12613, Giza, Egypt
| | - Ibrahim Elbatal
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
| | - Salem A. Alyami
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
| | - Ehab M. Almetwally
- Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
- Faculty of Business Administration, Delta University for Science and Technology, Gamasa, 11152, Egypt
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Huang M, Chen L, Ma J, Mo J, He L, Liang Q, Peng G, Tan Z. Biological functions of endophytic bacteria in Robinia pseudoacacia 'Hongsen '. Front Microbiol 2023; 14:1128727. [PMID: 37621396 PMCID: PMC10446884 DOI: 10.3389/fmicb.2023.1128727] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 07/17/2023] [Indexed: 08/26/2023] Open
Abstract
Introduction Endophytes and their host plants have co-evolved for a very long time. This relationship has led to the general recognition of endophytes as a particular class of microbial resources. R. pseudoacacia 'Hongsen' is drought- and barren-resistant species that can be grown in both the north and south of China, efficiently addresses the ecological issues caused by China's 'southern eucalyptus and northern poplar. Up to date, cultured-dependent studies are available for the R. pseudoacacia nitrogen-fixing and other endophytes. Therefore, the present research studied the R. pseudoacacia 'Hongsen,' microbiome in detail by high-throughput sequencing and culture dependant. Methods This study examined microbial species and functional diversity in Robinia pseudoacacia 'Hongsen' using culture-dependent (isolation) and culture-independent techniques. Results A total of 210 isolates were isolated from R. pseudoacacia 'Hongsen.' These isolates were clustered into 16 groups by the In Situ PCR (IS-PCR) fingerprinting patterns. 16S rRNA gene sequence analysis of the representative strain of each group revealed that these groups belonged to 16 species of 8 genera, demonstrating the diversity of endophytes in R. pseudoacacia 'Hongsen'. 'Bacillus is the most prevalent genus among all the endophytic bacteria. High-throughput sequencing of endophytic bacteria from R. pseudoacacia 'Hongsen' of the plant and the rhizosphere soil bacteria showed that the bacterial populations of soil near the root, leaf, and rhizosphere differed significantly. The microbial abundance decreased in the endophytes as compared to the rhizosphere. We observed a similar community structure of roots and leaves. With and without root nodules, Mesorhizobium sp. was significantly different in R. pseudoacacia 'Hongsen' plant. Discussion It was predicted that R. pseudoacacia 'Hongsen' plant endophytic bacteria would play a significant role in the metabolic process, such as carbohydrate metabolism, amino acid metabolism, membrane transport, and energy metabolism.
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Affiliation(s)
- Minqing Huang
- College of Agriculture, South China Agricultural University, Guangzhou, China
| | - Lijing Chen
- College of Agriculture, South China Agricultural University, Guangzhou, China
| | - Jiasi Ma
- College of Agriculture, South China Agricultural University, Guangzhou, China
| | - Jingzhi Mo
- College of Agriculture, South China Agricultural University, Guangzhou, China
| | - Lu He
- College of Agriculture, South China Agricultural University, Guangzhou, China
| | - Qihua Liang
- College of Natural Resources and Environment, South China Agricultural University, Guangzhou, China
| | - Guixiang Peng
- College of Natural Resources and Environment, South China Agricultural University, Guangzhou, China
| | - Zhiyuan Tan
- College of Agriculture, South China Agricultural University, Guangzhou, China
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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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Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040837] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stress–strength reliability in the case of two independent unit-half-normal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets.
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Abstract
The modeling different data behaviour like the human development index as a function of life expectancy, the water capacity of a reservoir with respect to a certain threshold, or the percentage of death rate of an infant before his or her first birthday, are situations which a researcher can face. It is noteworthy that these problems may have in common data with excessive zeros and ones. Then, it is essential to have flexible and accuracy models to fit data with these features. Given the relevance of data modeling with excessive zeros and ones, in this paper, a mixture of discrete and continuous distributions is proposed for modeling data with these behaviors. Additionally, the Unit-Birnbaum-Saunders distribution is considered with the aim to explain the continuous component of the model and the features of a Bernoulli process. The estimation of the parameters is based on the maximum likelihood method. Observed and expected information matrices are derived, illustrating interesting aspects of the likelihood approach. Finally, with practical applications by using real data we can show the advantage of using our proposal concerning the inflated beta model.
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Menezes AFB, Mazucheli J, de Oliveira RP, Chakraborty S. Improved maximum likelihood estimation of the parameters of the Gamma-Uniform distribution with bias-corrections. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1951760] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- A. F. B. Menezes
- Department of Statistics, Universidade Estadual de Maringá, DEs, Maringá, Paraná, Brazil
| | - J. Mazucheli
- Department of Statistics, Universidade Estadual de Maringá, DEs, Maringá, Paraná, Brazil
| | - R. P. de Oliveira
- Medical School, Universidade de São Paulo, Ribeirão Preto, Sao Paulo, Brazil
| | - S. Chakraborty
- Department of Statistics, Dibrugarh University, Dibrugarh, Assam, India
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Gedik Balay İ. Estimation of the generalized process capability index Cpyk based on bias-corrected maximum-likelihood estimators for the generalized inverse Lindley distribution and bootstrap confidence intervals. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1879081] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- İklim Gedik Balay
- Department of Banking and Finance, Ankara Yıldırım Beyazıt University, Ankara, Turkey
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Menezes AFB, Mazucheli J, Chakraborty S. A collection of parametric modal regression models for bounded data. J Biopharm Stat 2021; 31:490-506. [PMID: 34053398 DOI: 10.1080/10543406.2021.1918141] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Abstract
Modal regression is an alternative approach for investigating the relationship between the most likely response and covariates and can hence reveal important structure missed by usual regression methods. This paper provides a collection of parametric mode regression models for bounded response variable by considering some recently introduced probability distributions with bounded support along with the well-established Beta and Kumaraswamy distribution. The main properties of the distributions are highlighted and compared. An empirical comparison between the considered modal regression is demonstrated through the analysis of three data sets from health and social science. For reproducible research, the proposed models are freely available to users as an R package unitModalReg.
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Affiliation(s)
- André F B Menezes
- Departamento De Estatística, Universidade Estadual De Campinas, Campinas, Brasil
| | - Josmar Mazucheli
- Departamento De Estatística, Universidade Estadual De Maringá, Maringá, Brasil
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S. Rocha S, L. Espinheira P, Cribari‐Neto F. Residual and local influence analyses for unit gamma regressions. STAT NEERL 2020. [DOI: 10.1111/stan.12229] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Suelena S. Rocha
- Departamento de Estatística Universidade Federal de Pernambuco Recife PE Brazil
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Alotaibi RM, Tripathi YM, Dey S, Rezk HR. Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1806525] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Refah Mohammed Alotaibi
- Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
| | | | - Sanku Dey
- Department of Statistics, St. Anthony's College, Shillong, India
| | - Hoda Ragab Rezk
- Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
- Department of Statistics, Al-Azhar University, Cairo, Egypt
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Guerra RR, Peña-Ramírez FA, Bourguignon M. The unit extended Weibull families of distributions and its applications. J Appl Stat 2020; 48:3174-3192. [PMID: 35707261 PMCID: PMC9041710 DOI: 10.1080/02664763.2020.1796936] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2018] [Accepted: 07/12/2020] [Indexed: 10/23/2022]
Abstract
In this paper, two new general families of distributions supported on the unit interval are introduced. The proposed families include several known models as special cases and define at least twenty (each one) new special models. Since the list of well-being indicators may include several double bounded random variables, the applicability for modeling those is the major practical motivation for introducing the distributions on those families. We propose a parametrization of the new families in terms of the median and develop a shiny application to provide interactive density shape illustrations for some special cases. Various properties of the introduced families are studied. Some special models in the new families are discussed. In particular, the complementary unit Weibull distribution is studied in some detail. The method of maximum likelihood for estimating the model parameters is discussed. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Applications to the literacy rate in Brazilian and Colombian municipalities illustrate the usefulness of the two new families for modeling well-being indicators.
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Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters. Symmetry (Basel) 2020. [DOI: 10.3390/sym12060968] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
As a result of asymmetry in practical problems, the Lognormal distribution is more suitable for data modeling in biological and economic fields than the normal distribution, while biases of maximum likelihood estimators are regular of the order O ( n − 1 ) , especially in small samples. It is of necessity to derive logical expressions for the biases of the first-order and nearly consistent estimators by bias correction techniques. Two methods are adopted in this article. One is the Cox-Snell method. The other is the resampling method known as parametric Bootstrap. They can improve maximum likelihood estimators performance and correct biases of the Lognormal distribution parameters. Through Monte Carlo simulations, we obtain average root mean squared error and bias, which are two important indexes to compare the effect of different methods. The numerical results reveal that for small and medium-sized samples, the performance of analytical bias correction estimation is superior than bootstrap estimation and classical maximum likelihood estimation. Finally, an example is given based on the actual data.
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Menezes AFB, Mazucheli J. Improved maximum likelihood estimators for the parameters of the Johnson SB distribution. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2018.1498892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
| | - Josmar Mazucheli
- Department of Statistics, Universidade Estadual de Maringá, Maringá, PR, Brazil
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Ghitany ME, Mazucheli J, Menezes AFB, Alqallaf F. The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2018.1476717] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- M. E. Ghitany
- Faculty of Science, Department of Statistics and Operations Research, Kuwait University, Kuwait City, Kuwait
| | - J. Mazucheli
- Department of Statistics, Universidade Estadual de Maringá, DEs, PR, Brazil
| | - A. F. B. Menezes
- Department of Statistics, Universidade Estadual de Maringá, DEs, PR, Brazil
| | - F. Alqallaf
- Faculty of Science, Department of Statistics and Operations Research, Kuwait University, Kuwait City, Kuwait
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Mazucheli J, Menezes AFB, Dey S. Bias-corrected maximum likelihood estimators of the parameters of the inverse Weibull distribution. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1433838] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Josmar Mazucheli
- Department of Statistics, Universidade Estadual de Maringá Maringá, PR, Brazil
| | | | - Sanku Dey
- Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India
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