Bivariate Exponentiated Lomax Distribution Based on Marshall-olkin Method With a Real-life Application-Reference-Cited by-同舟云学术

Bivariate Exponentiated Lomax Distribution Based on Marshall-olkin Method With a Real-life Application

Published:2024-06-07 Issue: Volume: Page:
ISSN:
Container-title:
language:
Short-container-title:

Author:

Kalantan Z. I.¹,EL-Helbawy A. A.²,AL-Dayian Gannat²,Mahmoud Ahlam²,Refaey Reda²,Khalifa Mervat²

Affiliation:

1. King Abdulaziz University

2. AL-Azhar University

Abstract

This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Numerous attributes are examined, including the joint reliability and hazard functions, the bivariate probability density function, and its marginal. The joint probability density function and joint cumulative distribution function can be stated analytically. Different contour plots of the joint probability density function, joint reliability, joint hazard rate functions of the bivariate exponentiated Lomax distribution are given. The unknown parameters, reliability, and hazard rate functions of the bivariate exponentiated Lomax distribution are estimated using the maximum likelihood method. Also, Bayesian technique is applied to derive the Bayes estimators, reliability and hazard rate functions of the bivariate exponentiated Lomax distribution. In addition, maximum likelihood and Bayesian two-sample prediction is considered to predict a future observation from a future sample of the bivariate exponentiated Lomax distribution. Finally, a numerical illustration is presented, including a simulation study to investigate the theoretical findings derived in this paper of the maximum likelihood and Bayesian estimation. Also, a simulation study is provided to evaluate the theoretical outcomes and performance of the maximum likelihood and Bayesian predictors. Furthermore, the real data set used in this paper is the scoring times from 42 American Football League matches that took place over three consecutive independent weekends in 1986. The results of utilizing the real data approves the practicality and flexibility of the bivariate exponentiated Lomax distribution in real-world situations and that the bivariate exponentiated Lomax distribution is suitable for modeling this bivariate data set. Mathematics Subject Classification: 62F10, 62F15, 62N05, 62E10, 62N0

Publisher

Research Square Platform LLC

Reference1 articles.

1. Louzada, F., Suzuki, A. K., Cancho, V. G.: The FGM long-term bivariate survival copula model: modeling, Bayesian estimation, and case influence diagnostics. Commun. Stat. - Theory Metho. 42(4), 673–691 (2013).Denuit, M., Cornet, A.: Multiple premium calculation with dependent future lifetimes. JOAP, 7, 147–171 (1999).Marshall, A.W., Olkin, I.: A generalized bivariate exponential distribution. J. Appl. Probab. 291–302 (1967).Sarhan, A. M., Balakrishnan, N.: A new class of bivariate distributions and its mixture. J. Multivar. Anal. 98(7), 1508–1527 (2007).Kundu, D., Gupta, A.: Bayes estimation for the Marshall-Olkin bivariate Weibull distribution. CSDA. 57, 271–281 (2013).El-Gohary, A., El-Bassiouny, A. H. and El-Morshedy, M.: Bivariate exponentiated modified Weibull extension distribution. Stat. Appl. Probab. 5(1), 67–78 (2016).Aboraya, M.: A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications. Stat.., Optimiz. and inform. Comput., 9, 942–962 (2021).Shehata, W. A. M., Yousof, H. M., Aboraya, M.: A Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas. Pak.j.stat.oper.res. 17 (4) 943–961(2021).DOI: http://dx.doi.org/10.18187/pjsor.v17i4.3903Ali, M. M., Yousof, H. M. and Ibrahim, M.: A New Lomax Type Distribution: Properties, Copulas, Applications, Bayesian and Non-Bayesian Estimation Methods. International Journal of Statistical Sciences. 21(2), 61–104(2021).Tolba, A. H., Ramadan, D. A., Almetwally, E. M., Jawa, T. M., and Sayed, N. A.: Statistical Inference for Stress-Strength Reliability Using Inverse Lomax Lifetime Distribution with Mechanical Engineering Applications: Thermal Science, (26)1, S303-S326 (2022). https://doi.org/10.2298/TSCI22S1303T.Alotaibi, R., Al Mutairi, A., Almetwally, E. M., Park, C., Rezk, H.: Optimal Design for a Bivariate Step-Stress Accelerated Life Test with Alpha Power Exponential Distribution Based on Type-I Progressive Censored Samples. Symmetry, 14, 830 (2022). https://doi.org/10.3390/sym14040830.Alotaibi, N., Elbatal, I., Almetwally, E. M., Alyami, S. A., Al-Moisheer, A. S., Elgarhy, M.: Bivariate Step-Stress Accelerated Life Tests for the Kavya–Manoharan Exponentiated Weibull Model under Progressive Censoring with Applications. Symmetry, 14,1791(2022).https://doi.org/10.3390/sym14091791Shehata, W. A. M., Yousof, H. M.: A Novel Two-parameter Nadarajah-Haghighi Extension: Properties, Copulas, Modeling Real Data and Different Estimation Methods. Stat., Optimiz. and inform. Comput. (10) 725–749 (2022).Abdullah, M. M., Masmoudi, A.: Modeling Real-life Data Sets with a Novel G Family of Continuous Probability Distributions: Statistical Properties, and Copulas, Pak.j.stat.oper.res. 19(4), 719–746(2023).DOI: http://dx.doi.org/10.18187/pjsor.v19i4.2972. Refaie, M. K. A., Yaqoob, A. A., Selim, M. A., Ali E. I. A.: A Novel Version of the Exponentiated Weibull Distribution: Copulas, Mathematical Properties and Statistical Modeling. Pak.j.stat.oper.res. 19 (3) 491–519(2023).DOI: http://dx.doi.org/10.18187/pjsor.v19i3.4089 Refaie, M. K. A., Mahran, H. A.: A Novel Two-Parameter Compound G Family of Probability Distributions with Some Copulas, Statistical Properties and Applications. Stat., Optimiz. and inform. Comput., 11, 345–367(2023).Abbas, N.: On Classical and Bayesian Reliability of Systems Using Bivariate Generalized Geometric Distribution. Journal of Statistical Theory and Applications, 22, 151–169(2023).https://doi.org/10.1007/s44199-023-00058-4 Farooq, M., Gul A., Alshanbari, H. M., Khosa S. K.: Modeling of System Availability and Bayesian Analysis of Bivariate Distribution. Symmetry, 15, 1698 (2023). https://doi.org/10.3390/sym15091698Gupta, R. C., Gupta, P. L., Gupta, R. D.: Modeling failure time data by lehman alternatives. Commun. Stat. - Theory Meth., 27(4), 887–904 (1998).El-Monsef, M. M. E. A., Sweilam, N. H., Sabry, M. A.: The exponentiated power Lomax distribution and its applications. Qual Reliab Engng. Int., 37: 1035–1058 (2021). DOI:10.1002/qre.2780Almongy, H., Almetwally, E., Mubarak, A.: Marshall-Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics. Pakistan Journal of Statistics and Operation Research, 17, 137–153 (2021). DOI:10.18187/pjsor. v17i1.3402.Abd AL-Fattah, A. M., EL-Helbawy, A. A., AL-Dayian, G. R.: Inverted Kumaraswamy distribution: properties and estimation. Pakistan J. Stat. 33(1), 37–61 (2017).Mudholkar, G. S., Sriastava, D. K., Freimer, M.: The exponentiated Weibull family: a reanalysis of the bus motor failure data. Technometrics 37, 436–445 (1995).Abu-Zinadah, H. H.: A study on exponentiated Pareto distribution. Ph. D. Thesis, College of Education for Girls, Jeddah (2006).Shawky, A., Abu-Zinadah, H.: Characterizations of the exponentiated Pareto distribution based on record values. Appl. Math. Sci, 2(26), 1283–1290 (2008).AL-Dayian, G. R., Adham, S. A., El Beltagy, S. H., Abdelaal, M. K.: Bivariate half-logistic distributions Based on Mixtures and Copula. Acad. Bus. J. 2, 92–107 (2008).Kundu, D., Balakrishnan, N., Jamalizadeh, A.: Bivariate Birnbaum–Saunders distribution and associated inference. J. Multivar. Anal. 101(1), 113–125 (2010).Gupta, R. C., Kirmani, S., Srivastava, H.: Local dependence functions for some families of bivariate distributions and total positivity. Appl. Math. Comput. 216(4), 1267–1279 (2010).El-Sherpieny, E., Ibrahim, S., Bedar, R. E.: A New Bivariate Distribution with Generalized Gompertz Marginals. Asian J. Appl. Sci., 1(04) (2013).Capitani, L., Niclussi, F., Zini, A.: Trivariate Burr-III copula with applications to income data. METRON, Springer; Sapienza Università di Roma, 75(1), 109–124 (2016).Al-erwi, A. S., Baharith, L. A.: A bivariate exponentiated Pareto distribution derived from Gaussian copula. Int. j. adv. appl. 4(7), 66–73 (2017).Ogana, F. N., Osho, J. S. A., Gorgoso-Varela, J. J.: An approach to modeling the joint distribution of tree diameter and height data. J. Sustain. For. 37(5), 475–488 (2018).Azizi, A., Syyareh, A.: Estimating the parameters of the bivariate Burr III distribution by EM algorithm. J. Iran. 18(1), 133–155 (2019).Mondal, S., Kundu, D.: A bivariate inverse Weibull distribution and its application in complementary risks model. J. Appl. Stat. (2019). doi:10.1080/02664763.2019.1669542.Bakouch, H. S., Moala, F. A., Saboor, A., Samad, H.: A bivariate Kumaraswamy exponential distribution with application. Math. Slovaca. (2019). DOI: 10.1515/ms-2017-0300.Kamal, M., Aldallal, R., Nassr, S. G., Al Mutairi, A., Yusuf, M., Mustafa, M. S., Alsolmi, M. M., Almetwally, E. M.: A new improved form of the Lomax model: Its bivariate extension and an application in the financial sector, Alexandria Engineering Journal, 75, 127–138 (2023). DOI: 10.1016/j.aej.2023.05.027.Aljohani, H. M.: Estimation for the P (X > Y) of Lomax distribution under accelerated life tests, Heliyon, 10(3), e25802 (2024), DOI: 10.1016/j.heliyon.e25802 (2024).Elgohari, H., Yousof, H. M.: A Generalization of Lomax Distribution with Properties, Copula and Real Data Applications. Pak.j.stat.oper.res. 16 (4) 697–711(2020).DOI: http://dx.doi.org/10.18187/pjsor.v16i4.3260Hamed, M., S., Cordeiro, G. M., Yousof, H. M.: A New Compound Lomax Model: Properties, Copulas, Modeling and Risk Analysis Utilizing the Negatively Skewed Insurance Claims Data. Pak.j.stat.oper.res. 18 (3), 601–631(2022).DOI: http://dx.doi.org/10.18187/pjsor.v18i3.365Aboraya, M., Ali, M. M., Yousof, H. M., Ibrahim, M.: A Novel Lomax Extension with Statistical Properties, Copulas, Different Estimation Methods and Applications. Bulletin of the Malaysian Mathematica Sciences Society, 45 (1): S85–S120(2022).https://doi.org/10.1007/s40840-022-01250-yEl-Sherpieny, E. S. A., Muhammed, H. Z., and Almetwally, E. M.: Data Analysis by Adaptive Progressive Hybrid Censored Under Bivariate Model. Annals of Data Science, 1–42(2022). https://doi.org/10.1007/s40745-022-00455-z El-Sherpieny, E. S. A., Muhammed, H. Z., and Almetwally, E. M.: Bivariate Chen Distribution Based on Copula Function: Properties and Application of Diabetic Nephropathy. Journal of Statistical Theory and Practice, 16(3), 54(2022). https://doi.org/10.1007/s42519-022-00275-7El-Sherpieny, E. S. A., Muhammed, H. Z., and Almetwally, E. M.: Accelerated Life Testing for Bivariate Distributions based on Progressive Censored Samples with Random Removal. J. Stat. Appl. Probab, 11(2), 203–223(2022).Almetwally, E. M., and Muhammed, H. Z.: On a bivariate Fréchet distribution. Journal Statistics Applications Probability, 9, 1–21(2020).El-Sherpieny, E. S. A., Almetwally, E. M., and Muhammed H. Z.: Bivariate Weibull-g family based on copula function: properties, Bayesian and non-Bayesian estimation and applications. Stat., Optimiz. and inform. Comput., 10(3), 678–709(2022). https://doi.org/10.19139/soic-2310-5070-1129Muhammed, H. Z., El-Sherpieny, E. S. A., and Almetwally, E. M.: Dependency measures for new bivariate models based on copula function. Information Sciences Letters, 10, 511–526 (2021). http://dx.doi.org/10.18576/isl/100316Abulebda, M., Pathak, A. K., Pandey, A., and Tyagi, S.: On a Bivariate XGamma Distribution Derived from Copula. Statistica, 82, 15–40 (2022).Hassan, M. K., and Chesneau, C.: Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA. Mathematical and Computational Applications, 27, 72 (2022).https://doi.org/10.3390/mca27040072Zhao, J., Faqiri, H., Ahmad, Z., Emam W., Yusuf, M., and Sharawy, A. M.: The lomax-claim model: bivariate extension and applications to financial data. Complexity, 1–17(2021).Qura, M. E., Fayomi A., Kilai, M., Almetwally, E. M.: Bivariate power Lomax distribution with medical applications. PLoS ONE 18(3): e0282581(2023).https://doi.org/10.1371/journal.pone.0282581Hamedani, G.: Characterizations of exponentiated distributions. Pak. J. Stat. Oper. IX (1), 17–24 (2013).Basu, A. P.: Bivariate failure rate. J. Am. Stat. Assoc. 66, 103–104 (1971).Pena, A. and Gupta, A. K.: Bayes estimation for the Marshall-Olkin exponential distribution. J. R. Stat. Soc. Series B. 52(2), 379–389 (1990).Csorgo, S., Welsh, A. H.: Testing for exponential and Marshall-Olkin distribution. J. Stat. Plan Inference. 23, 287–300 (1989).