{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T02:58:25Z","timestamp":1764212305753,"version":"build-2065373602"},"reference-count":84,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T00:00:00Z","timestamp":1690243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Imam Muhammad ibn Saud Islamic University","award":["221412039"],"award-info":[{"award-number":["221412039"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp\u2013Leone (PTL) distribution called the Kavya\u2013Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual R\u00e9nyi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp\u2013Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.<\/jats:p>","DOI":"10.3390\/axioms12080722","type":"journal-article","created":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T01:09:01Z","timestamp":1690333741000},"page":"722","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp\u2013Leone Distribution under Ranked Set Sampling with Applications"],"prefix":"10.3390","volume":"12","author":[{"given":"Naif","family":"Alotaibi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2764-686X","authenticated-orcid":false,"given":"A. S.","family":"Al-Moisheer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jouf University, P.O. Box 848, Sakaka 72351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibrahim","family":"Elbatal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3456-8393","authenticated-orcid":false,"given":"Mansour","family":"Shrahili","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/01621459.1955.10501259","article-title":"A Family of J-Shaped Frequency Functions","volume":"50","author":"Topp","year":"1955","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_2","first-page":"1005","article-title":"Topp-Leone inverse Weibull distribution: Theory and application","volume":"10","author":"Abbas","year":"2017","journal-title":"Eur. J. Pure App. Math."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"ZeinEldin, R.A., Chesneau, C., Jamal, F., and Elgarhy, M. (2019). Different Estimation Methods for Type I Half-Logistic Topp-Leone Distribution. Mathematics, 7.","DOI":"10.3390\/math7100985"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sudsuk, A., and Bodhisuwan, W. (2016, January 4\u20136). The Topp-Leone geometric distribution. Proceedings of the 12th International Conference on Mathematics, Statistics, and Their Applications (ICMSA), Banda Aceh, Indonesia.","DOI":"10.1109\/ICMSA.2016.7954319"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mohamed, R.A.H., Elgarhy, M., Alabdulhadi, M.H., Almetwally, E.M., and Radwan, T. (2023). Statistical Inference of Truncated Cauchy Power-Inverted Topp-Leone Distribution under Hybrid Censored Scheme with Applications. Axioms, 12.","DOI":"10.3390\/axioms12020148"},{"key":"ref_6","first-page":"119","article-title":"Topp-Leone Nadarajah-Haghighi distribution","volume":"10","author":"Yousof","year":"2017","journal-title":"\u0130statistik\u00e7iler Dergisi \u0130statistik ve Akt\u00fcerya"},{"key":"ref_7","first-page":"991","article-title":"Power inverted Topp-Leone distribution in acceptance sampling plans","volume":"67","author":"Abushal","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1515\/eqc-2017-0022","article-title":"Topp\u2013Leone linear exponential distribution","volume":"33","author":"Atem","year":"2018","journal-title":"Stoch. Qual. Cont."},{"key":"ref_9","first-page":"337","article-title":"Kumaraswamy inverted Topp-Leone distribution with applications to COVID-19 data","volume":"68","author":"Hassan","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bantan, R.A., Jamal, F., Chesneau, C., and Elgarhy, M. (2019). A new power Topp-Leone generated family of distributions with applications. Entropy, 21.","DOI":"10.3390\/e21121177"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"353","DOI":"10.32604\/iasc.2021.017586","article-title":"Parameter estimation of alpha power inverted Topp-Leone distribution with applications","volume":"29","author":"Ibrahim","year":"2021","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bantan, R., Elsehetry, M., Hassan, A.S., Elgarhy, M., Sharma, D., Chesneau, C., and Jamal, F. (2021). A Two-Parameter Model: Properties and Estimation under Ranked Sampling. Mathematics, 9.","DOI":"10.3390\/math9111214"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bantan, R.A., Jamal, F., Chesneau, C., and Elgarhy, M. (2020). Type II power Topp-Leone generated family of distributions with statistical inference and applications. Symmetry, 12.","DOI":"10.3390\/sym12010075"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1007\/s00180-017-0780-9","article-title":"The odd log-logistic Topp-Leone G family of distributions: Heteroscedastic regression models and applications","volume":"33","author":"Alizadeh","year":"2018","journal-title":"Comput. Stat."},{"key":"ref_15","first-page":"437","article-title":"Topp-Leone odd Fr\u00e9chet generated family of distributions with applications to Covid-19 datasets","volume":"125","author":"Jamal","year":"2020","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e06534","DOI":"10.1016\/j.heliyon.2021.e06534","article-title":"The Burr III-Topp-Leone-G family of distributions with applications","volume":"7","author":"Chipepa","year":"2021","journal-title":"Heliyon"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"319","DOI":"10.18576\/jsap\/090212","article-title":"Statistical properties and estimation of inverted Topp-Leone Distribution","volume":"9","author":"Hassan","year":"2020","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18187\/pjsor.v15i1.2166","article-title":"The Exponentiated Generalized Topp Leone-G Family of Distributions: Properties and Applications","volume":"15","author":"Reyad","year":"2019","journal-title":"Pak. J. Stat. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.18576\/jsap\/100120","article-title":"Transmuted Topp-Leone power function distribution: Theory and application","volume":"10","author":"Hassan","year":"2021","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"723","DOI":"10.6339\/JDS.201710_15(4).00008","article-title":"The transmuted Topp-Leone G family of distributions: Theory, characterizations and applications","volume":"15","author":"Yousof","year":"2017","journal-title":"J. Data Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1515\/phys-2020-0180","article-title":"Sine Topp-Leone-G family of distributions: Theory and applications","volume":"18","author":"Elbatal","year":"2020","journal-title":"Open Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.15672\/hujms.795721","article-title":"A weighted Topp-Leone G family of distributions: Properties, applications for modelling reliability data and different method of estimation","volume":"51","author":"Hashempour","year":"2022","journal-title":"Stat. Hacett. J. Math. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.35378\/gujs.773645","article-title":"Estimation of parameters of Topp-Leone inverse Lomax distribution in presence of right-censored samples","volume":"34","author":"Hassan","year":"2021","journal-title":"Gazi Uni. J. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"615","DOI":"10.19139\/soic-2310-5070-1514","article-title":"A new Weighted Topp-Leone Family of Distributions","volume":"11","author":"Shaheed","year":"2023","journal-title":"Stat. Optim. Inf. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"731","DOI":"10.35378\/gujs.776277","article-title":"Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution","volume":"35","author":"Elgarhy","year":"2022","journal-title":"Gazi Uni. J. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Aidi, K., Al-Omari, A.I., and Alsultan, R. (2022). The Power Zeghdoudi Distribution: Properties, Estimation, and Applications to Real Right-Censored Data. Appl. Sci., 12.","DOI":"10.3390\/app122312081"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Afify, A.Z., Gemeay, A.M., Alfaer, N.M., Cordeiro, G.M., and Hafez, E.H. (2022). Power-Modified Kies-Exponential Distribution: Properties, Classical and Bayesian Inference with an Application to Engineering Data. Entropy, 24.","DOI":"10.3390\/e24070883"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Al-Omari, A.I., Aidi, K., and Alsultan, R. (2022). Power Darna distribution with right censoring: Estimation, testing, and applications. Appl. Sci., 12.","DOI":"10.3390\/app12168272"},{"key":"ref_29","first-page":"27","article-title":"The power Burr Type X distribution: Properties, regression modeling and applications","volume":"52","author":"Usman","year":"2020","journal-title":"Punjab Univ. J. Math."},{"key":"ref_30","first-page":"1","article-title":"Statistical properties and estimation of power-transmuted inverse Rayleigh distribution","volume":"21","author":"Hassan","year":"2020","journal-title":"Stat. Trans. New Ser."},{"key":"ref_31","first-page":"6","article-title":"A two-parameter power Rama distribution with properties and applications","volume":"8","author":"Abebe","year":"2019","journal-title":"Biom. Biostat. Int. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3042","DOI":"10.1080\/03610918.2017.1367807","article-title":"Power binomial exponential distribution: Modeling, simulation and application","volume":"47","author":"Habibi","year":"2018","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"210","DOI":"10.5958\/1945-919X.2018.00016.6","article-title":"A two-parameter power Aradhana distribution with properties and application","volume":"9","author":"Shanker","year":"2018","journal-title":"Indian Soc. Ind. Appl. Math."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1838","DOI":"10.1186\/s40064-016-3464-y","article-title":"The power Lomax distribution with an application to bladder cancer data","volume":"5","author":"Rady","year":"2016","journal-title":"SpringerPlus"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2084236","DOI":"10.1155\/2016\/2084236","article-title":"On a power transformation of half-logistic distribution","volume":"2016","author":"Krishnarani","year":"2016","journal-title":"J. Probab. Stat."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"175","DOI":"10.5336\/biostatic.2017-56601","article-title":"Power Shanker distribution and its application","volume":"9","author":"Shanker","year":"2017","journal-title":"Turk. Klin. Biyoistatistik"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.csda.2013.02.026","article-title":"Power Lindley distribution and associated inference","volume":"64","author":"Ghitany","year":"2013","journal-title":"Comput. Stat. Data. Anal."},{"key":"ref_38","unstructured":"Rooks, B., Schumacher, A., and Cooray, K. (2023, May 25). The Power Cauchy Distribution: Derivation, Description, and Composite Models; NSF-REU Program Reports. Available online: http:\/\/www.cst.cmich.edu\/mathematics\/research\/REU_and_LURE.shtml."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3693","DOI":"10.1080\/00949655.2021.1946064","article-title":"Some parsimonious models for lifetimes and applications","volume":"91","author":"Kavya","year":"2021","journal-title":"J. Statist. Comput. Simul."},{"key":"ref_40","first-page":"1891","article-title":"New ranked set sampling for estimating the population mean and variance","volume":"45","author":"Zamanzade","year":"2016","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1080\/00949655.2019.1604710","article-title":"A new sampling method for estimating the population mean","volume":"89","author":"Haq","year":"2019","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Nagy, H.F., Al-Omari, A.I., Hassan, A.S., and Alomani, G.A. (2022). Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data. Mathematics, 10.","DOI":"10.3390\/math10214102"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Alghamdi, S.M., Bantan, R.A.R., Hassan, A.S., Nagy, H.F., Elbatal, I., and Elgarhy, M. (2022). Improved EDF-Based Tests for Weibull Distribution Using Ranked Set Sampling. Mathematics, 10.","DOI":"10.3390\/math10244700"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Hassan, A.S., Almanjahie, I.M., Al-Omari, A.I., Alzoubi, L., and Nagy, H.F. (2023). Stress-Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application. Mathematics, 11.","DOI":"10.3390\/math11020318"},{"key":"ref_45","first-page":"37","article-title":"Parameter estimation of exponentiated exponential distribution under selective ranked set sampling","volume":"23","author":"Hassan","year":"2022","journal-title":"Stat. Transit."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Al-Omari, A.I., Benchiha, S., and Almanjahie, I.M. (2022). Efficient estimation of two-parameter Xgamma distribution parameters using ranked set sampling design. Mathematics, 10.","DOI":"10.3390\/math10173170"},{"key":"ref_47","first-page":"835","article-title":"Estimation of the stress-strength reliability for exponentiated Pareto distribution using median and ranked set sampling methods","volume":"64","author":"Almanjahie","year":"2020","journal-title":"Comput. Mater. Contin."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Khamnei, H.J., Meidute-Kavaliauskiene, I., Fathi, M., Valackien\u0117, A., and Ghorbani, S. (2022). Parameter estimation of the exponentiated Pareto distribution using ranked set sampling and simple random sampling. Axioms, 11.","DOI":"10.3390\/axioms11060293"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Jiang, H., and Gui, W. (2021). Bayesian inference for the parameters of Kumaraswamy distribution via ranked set sampling. Symmetry, 13.","DOI":"10.3390\/sym13071170"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"11099","DOI":"10.1016\/j.aej.2022.04.040","article-title":"Estimation of the Kumaraswamy distribution parameters using the E-Bayesian method","volume":"61","author":"Alduais","year":"2022","journal-title":"Alex. Eng. J."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1080\/03610926.2019.1639745","article-title":"Parameter estimation for the exponential-Poisson distribution based on ranked set samples","volume":"50","author":"Joukar","year":"2021","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1080\/03610926.2019.1705977","article-title":"Estimation of the system reliability for generalized inverse Lindley distribution based on different sampling designs","volume":"50","author":"Akgul","year":"2020","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1080\/00949655.2020.1814287","article-title":"Estimation based on ranked set sampling for the two-parameter Birnbaum-Saunders distribution","volume":"91","author":"Pedroso","year":"2021","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_54","first-page":"9982397","article-title":"Efficient estimation of the generalized Quasi-Lindley distribution parameters under ranked set sampling and applications","volume":"2021","author":"Benchiha","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2533","DOI":"10.1080\/03610920903061039","article-title":"Bayes Estimation of Weibull Distribution Parameters Using Ranked Set Sampling","volume":"39","author":"Helu","year":"2010","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_56","first-page":"2169","article-title":"Zubair Lomax distribution: Properties and estimation based on ranked set sampling","volume":"65","author":"Bantan","year":"2020","journal-title":"CMC-Comput. Mater. Contin."},{"key":"ref_57","unstructured":"R\u00e9nyi, A. (July, January 30). On measures of entropy and information. Proceedings of the 4th Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0019-9958(71)90065-9","article-title":"Information-theoretical considerations on estimation problems","volume":"19","author":"Arimoto","year":"1971","journal-title":"Inf. Control"},{"key":"ref_59","first-page":"547","article-title":"The role of constraints within generalized non-extensive statistics","volume":"261","author":"Tsallis","year":"1998","journal-title":"Physica"},{"key":"ref_60","first-page":"30","article-title":"Quantification method of classification processes, Concept of Structural Entropy","volume":"3","author":"Havrda","year":"1967","journal-title":"Kybernetika"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1109\/TIT.2004.828057","article-title":"Cumulative residual entropy: A new measure of information","volume":"50","author":"Rao","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1071\/AR9520385","article-title":"A method for unbiased selective sampling, using ranked sets","volume":"3","author":"McIntyre","year":"1952","journal-title":"Aust. J. Agric. Res."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02911622","article-title":"On unbiased estimates of the population mean based on the sample stratified by means of ordering","volume":"20","author":"Takahasi","year":"1968","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Alotaibi, N., Al-Moisheer, A.S., Elbatal, I., Shrahili, M., Elgarhy, M., and Almetwally, E.M. (2023). Half Logistic Inverted Nadarajah\u2013Haghighi Distribution under Ranked Set Sampling with Applications. Mathematics, 11.","DOI":"10.3390\/math11071693"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Alotaibi, N., Elbatal, I., Shrahili, M., Al-Moisheer, A.S., Elgarhy, M., and Almetwally, E.M. (2023). Statistical inference for the Kavya-Manoharan Kumaraswamy model under ranked set sampling with applications. Symmetry, 15.","DOI":"10.3390\/sym15030587"},{"key":"ref_66","first-page":"3737","article-title":"Assessing the Performance of Some Ranked Set Sampling Designs Using Hybrid Approach","volume":"68","author":"Sabry","year":"2021","journal-title":"Comput. Mater. Conti."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"108136","DOI":"10.1016\/j.ress.2021.108136","article-title":"Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints","volume":"218 Pt A","author":"Luo","year":"2022","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1103\/RevModPhys.83.943","article-title":"Bayesian inference in physics","volume":"83","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Eldessouky, E.A., Hassan, O.H.M., Elgarhy, M., Hassan, E.A., Elbatal, I., and Almetwally, E.M. (2023). A New Extension of the Kumaraswamy Exponential Model with Modeling of Food Chain Data. Axioms, 12.","DOI":"10.3390\/axioms12040379"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1093\/ije\/dyl289","article-title":"Bayesian perspectives for epidemiological research. II. Regression analysis","volume":"36","author":"Greenland","year":"2007","journal-title":"Int. J. Epidem."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1016\/j.envsoft.2011.06.004","article-title":"Bayesian networks in environmental modelling","volume":"26","author":"Aguilera","year":"2011","journal-title":"Environ. Model. Softw."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"e287","DOI":"10.1097\/INF.0000000000003204","article-title":"A Bayesian model to predict COVID-19 severity in children","volume":"40","author":"Villaverde","year":"2021","journal-title":"Pediatr. Infect. Dis. J."},{"key":"ref_73","unstructured":"Chan, J., and Tobias, J.L. (2021). Handbook of Labor, Human Resources and Population Economics, Springer International Publishing."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Zhou, S., Xu, A., Tang, Y., and Shen, L. (2023). Fast Bayesian Inference of Reparameterized Gamma Process With Random Effects. IEEE Trans. Reliab.","DOI":"10.1109\/TR.2023.3263940"},{"key":"ref_75","first-page":"7","article-title":"CODA: Convergence diagnosis and output analysis for MCMC","volume":"6","author":"Plummer","year":"2006","journal-title":"R News"},{"key":"ref_76","unstructured":"Meredith, M., and Kruschke, J. (2023, March 20). HDInterval: Highest (Posterior) Density Intervals. R Package Version 0.1. Available online: https:\/\/cran.r-project.org\/web\/packages\/HDInterval\/index.html."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of state calculations by fast computing machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","article-title":"Monte Carlo sampling methods using Markov chains and their applications","volume":"57","author":"Hastings","year":"1970","journal-title":"Biometrika"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1080\/01621459.1990.10476213","article-title":"Sampling-based approaches to calculating marginal densities","volume":"85","author":"Gelfand","year":"1990","journal-title":"J. Amer. Stat. Assoc."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/10618600.1999.10474802","article-title":"Monte Carlo estimation of Bayesian credible and HPD intervals","volume":"8","author":"Chen","year":"1999","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"2074","DOI":"10.1002\/sim.8086","article-title":"Using simulation studies to evaluate statistical methods","volume":"38","author":"Morris","year":"2019","journal-title":"Stat. Med."},{"key":"ref_82","unstructured":"Stock, J.H., and Watson, M.W. (2007). Introduction to Econometrics, Addison Wesley. [2nd ed.]. Available online: Https:\/\/rdrr.io\/cran\/AER\/man\/GrowthSW.html."},{"key":"ref_83","first-page":"25","article-title":"Unit-Gompertz distribution with applications","volume":"79","author":"Mazucheli","year":"2019","journal-title":"Statistica"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1080\/00949658008810388","article-title":"Concentration bands for uniformity plots","volume":"11","author":"Quesenberry","year":"1980","journal-title":"J. Stat. Comput. 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