Abstract
The purpose of this paper is to introduce the adaptive progressive hybrid censored scheme of the bivariate model which expands the limited applicability of failure censored schemes for the bivariate models in several fields of products. Also, the paper discusses a new bivariate model based on an adaptive progressive hybrid censored with more efficacy than the traditional models. Based on the FGM copula function and Odd-Weibull family, we will introduce the bivariate FGM Weibull-Weibull distribution. To estimate the model parameters, maximum likelihood and Bayesian estimation are used. In addition, for the parameter model, asymptotic confidence intervals and credible intervals of the highest posterior density for the Bayesian are calculated. A Monte-Carlo simulation analysis is carried out of the maximum likelihood and Bayesian estimators. Finally, we demonstrate the utility of the suggested bivariate distribution using real data from the medical area, such as diabetic nephropathy data.
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Data Availability
The data is included in Section Application of Diabetic Nephropathy Data.
References
Hassan AS, Abd-Allah M (2019) On the inverse power Lomax distribution. Ann Data Sci. 6(2):259–278
Almetwally EM (2022) Marshall olkin alpha power extended Weibull distribution: different methods of estimation based on type i and type II censoring. Gazi Univ J Sci 35(1):293–312
Balakrishnan N, Cramer E (2014) The art of progressive censoring. Stat Ind Technol
Ng HKT, Kundu D, Chan PS (2009) Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme. Nav Res Logist 56(8):687–698
Balakrishnan N, Kundu D (2013) Hybrid censoring: models, inferential results and applications. Comput Stat Data Anal 57(1):166–209
Lin CT, Huang YL (2012) On progressive hybrid censored exponential distribution. J Stat Comput Simul 82(5):689–709
Balakrishnan N, Kim JA (2004) EM algorithm for Type-II right censored bivariate normal data. In: Parametric and semiparametric models with applications to reliability, survival analysis, and quality of life (pp. 177-210). Birkhäuser, Boston, MA
Balakrishnan N, Kim JA (2005) Point and interval estimation for bivariate normal distribution based on progressively Type-II censored data. Commun Stat Theory Methods 34(6):1297–1347
Balakrishnan N, Kim JA (2005) EM algorithm and optimal censoring schemes for progressively Type-II censored bivariate normal data. In: Advances in ranking and selection, multiple comparisons, and reliability (pp. 21-45). Birkhäuser Boston
Kim SW, Ng HKT, Jang H (2016) Estimation of parameters in a bivariate generalized exponential distribution based on Type-II censored samples. Commun Stat Simul Comput 45(10):3776–3797
Aly HM, Muhammed HZ, Abuelamayem OA (2020) Estimation of the bivariate Kumaraswamy lifetime distribution under progressive type-I censoring. J Data Sci 18(4):739–749
El-Morshedy M, Alhussain ZA, Atta D, Almetwally EM, Eliwa MS (2020) Bivariate Burr X generator of distributions: properties and estimation methods with applications to complete and type-II censored samples. Mathematics 8(2):264
El-Sherpieny ESA, Almetwally EM, Muhammed HZ (2021) Bayesian and non-bayesian estimation for the parameter of bivariate generalized Rayleigh distribution based on clayton copula under progressive type-II censoring with random removal. Sankhya A, 1-38
Muhammed HZ, Almetwally EM (2020) Bayesian and non-Bayesian estimation for the bivariate inverse weibull distribution under progressive type-II censoring. Ann Data Sci. https://doi.org/10.1007/s40745-020-00316-7
Shi Yong (2022) Advances in big data analytics. Theory, algorithm and practice. Springer, Singapore
Zhao P, Zhao X, Zhao C (2020) Image denoising based on bivariate distribution. Symmetry 12(11):1909
Dehghani H, Fadaee MJ (2020) Probabilistic prediction of earthquake by bivariate distribution. Asian J Civ Eng 21:977–983
Sarabia JM, Prieto F, Jordá V (2014) Bivariate beta-generated distributions with applications to well-being data. J Stat Distrib Appl 1(1):1–26
Sankaran PG, Nair NU (1993) A bivariate Pareto model and its applications to reliability. Nav Res Logist 40(7):1013–1020
Krishna H, Pundir PS (2009) A bivariate geometric distribution with applications to reliability. Commun Stat Theory Methods 38(7):1079–1093
Sankaran PG, Lawless JF, Abraham B, Antony AA (2006) Estimation of distribution function in bivariate competing risk models. Biom J 48(3):399–410
Lai X, Yau KK, Liu L (2017) Competing risk model with bivariate random effects for clustered survival data. Comput Stat Data Anal 112:215–223
Kızılaslan F, Nadar M (2018) Estimation of reliability in a multicomponent stress-strength model based on a bivariate Kumaraswamy distribution. Stat Pap 59(1):307–340
Mirabbasi R, Fakheri-Fard A, Dinpashoh Y (2012) Bivariate drought frequency analysis using the copula method. Theor Appl Climatol 108(1):191–206
Franco M, Vivo JM, Kundu D (2020) A generator of bivariate distributions: properties, estimation, and applications. Mathematics 8(10):1776
El-Sherpieny ESA, Muhammed HZ, Almetwally EM (2021) Bivariate Weibull-G family based on Copula function: properties, Bayesian and non-Bayesian estimation and applications. Stat Optim Inf Comput. https://doi.org/10.19139/soic-2310-5070-1129
Darwish JA, Al Turk LI, Shahbaz MQ (2021) Bivariate transmuted burr distribution: properties and application. Pak J Stat Oper Res 17(1):15–24
Bentoumi R, El Ktaibi F, Mesfioui M (2021) A new family of bivariate exponential distributions with negative dependence based on counter-monotonic shock method. Entropy 23(5):548
El-Sherpieny ES, Almetwally EM (2019) Bivariate generalized rayleigh distribution based on Clayton Copula. In: Proceedings of the annual conference on statistics (54rd), computer science and operation research, faculty of graduate studies for statistical research, Cairo University (pp. 1-19)
Almetwally EM, Muhammed HZ (2020) On a bivariate Fréchet distribution. J Stat Appl Probab 9(1):1–21
Almetwally EM, Muhammed HZ, El-Sherpieny ESA (2020) Bivariate Weibull distribution: properties and different methods of estimation. Ann Data Sci 7(1):163–193
Muhammed HZ (2016) Bivariate inverse Weibull distribution. J Stat Comput Simul 86(12):2335–2345
Sklar A (1973) Random variables, joint distribution functions, and copulas. Kybernetika 9(6):449–460
Gumbel EJ (1960) Bivariate exponential distributions. J Am Stat Assoc 55(292):698–707
Almetwally EM (2019) Parameter estimation of bivariate models under some censoring schemes, Master Thesis, Faculty of Graduate Studies for Statistical Research, Cairo University
Shi Y (2022) Advances in big data analytics: theory, algorithms and practices. Springer, Cham
Deng W, Patil R, Liu F, Daji E, Shi Y (2022) Exploring freight loading management by deep learning: a case study in home furnishing industry. Ann Data Sci 9(2):213–228
Olson DL, Shi Y, Shi Y (2007) Introduction to business data mining, vol 10. McGraw-Hill/Irwin, New York, pp 2250–2254
Shi Y, Tian Y, Kou G, Peng Y, Li J (2011) Optimization based data mining: theory and applications. Springer, Cham
Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178
Yang SS (1977) General distribution theory of the concomitants of order statistics. Ann Stat 5(5):996–1002
David HA, Galambos J (1974) The asymptotic theory of concomitants of order statistics. J Appl Probab 11(4):762–770
Tse SK, Yang C, Yuen HK (2000) Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals. J Appl Stat 27(8):1033–1043
Suzuki AK, Louzada-Neto F, Cancho VG, Barriga GD (2011) The FGM bivariate lifetime copula model: a Bayesian approach. Adv Appl Stat 21(1):55–76
Louzada F, Suzuki AK, Cancho VG (2013) The FGM long-term bivariate survival copula model: modeling, Bayesian estimation, and case influence diagnostics. Commun Stat Theory Methods 42(4):673–691
Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69–92
Luengo D, Martino L, Bugallo M, Elvira V, Särkkä S (2020) A survey of Monte Carlo methods for parameter estimation. Eurasip J Adv Signal Process 2020(1):1–62
Nelsen RB (2007) An introduction to copulas. Springer, Cham
Grover G, Sabharwal A, Mittal J (2014) Application of multivariate and bivariate normal distributions to estimate duration of diabetes. Int J Stat Appl 4(1):46–57
Genest C, Rémillard B, Beaudoin D (2009) Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ 44:199–214
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The authors wish to thank the editor. We also thank anonymous for their encouragement and support. The authors are grateful to anyone reviewed the paper carefully and for their helpful comments that improve this paper.
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Conceptualization by EAES, and HZM; Supervision by EAES, and HZM; Resources by EMA; Software by EMA; Writing and original draft by EMA; Writing, review, and editing by EAES, and HZM.
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Function “maxlik” of “maxLik” package and “copula” package in the R program has been used.
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El-Sherpieny, ES.A., Muhammed, H.Z. & Almetwally, E.M. Data Analysis by Adaptive Progressive Hybrid Censored Under Bivariate Model. Ann. Data. Sci. 11, 507–548 (2024). https://doi.org/10.1007/s40745-022-00455-z
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DOI: https://doi.org/10.1007/s40745-022-00455-z