Exponentiated UEHL Distribution: Properties and Applications

Yıl 2023, , 232 - 241, 31.12.2023

Murat Genç , Ömer Özbilen

https://doi.org/10.53501/rteufemud.1388416

Cited By: 1

Öz

In this paper, we propose a distribution for modeling data defined on a unit interval using an exponentiated transformation. The new distribution is based on the unit exponential half-logistic distribution, a member of proportional hazard models. Several measures of the statistical characterization of the distribution are discussed. The statistical inference of the parameters of the proposed distribution is studied by the maximum likelihood method. To explore the properties of the maximum likelihood estimates of the parameters, simulation studies are carried out under various scenarios. Furthermore, a real dataset is analyzed to demonstrate the performance of the distribution.

Anahtar Kelimeler

Exponentiated distribution, UEHL distribution, maximum likelihood estimator, goodness of fit

Üstellenmiş UEHL Dağılımı: Özellikler ve Uygulamalar

Öz

Bu makalede, birim aralıkta tanımlanan verilerin üstel bir dönüşüm kullanılarak modellenmesi için bir dağılım önerilmiştir. Yeni dağılım, orantılı tehlike modellerinin bir üyesi olan birim üstel yarı lojistik dağılıma dayanmaktadır. Dağılımın istatistiksel karakterizasyonuna ilişkin çeşitli ölçütler tartışılmıştır. Önerilen dağılımın parametrelerinin istatistiksel çıkarımı en çok olabilirlik yöntemi ile incelenmiştir. Parametrelerin en çok olabilirlik tahminlerinin özelliklerini araştırmak için çeşitli senaryolar altında simülasyon çalışmaları gerçekleştirilmiştir. Ayrıca, dağılımın performansını göstermek için gerçek bir veri kümesi analiz edilmiştir.

Anahtar Kelimeler

Üstellenmiş dağılım, UEHL dağılımı, en çok olabilirlik tahmin edicisi, uyum iyiliği

Kaynakça

• Almalki, S.J., Nadarajah, S. (2014). Modifications of the Weibull distribution: A review. Reliability Engineering and System Safety, 124, 32-55. https://doi.org/10.1016/j.ress.2013.11.010
• Alotaibi, R., Okasha, H., Nassar, M., Elshahhat, A. (2023). A novel modified alpha power transformed weibull distribution and its engineering applications. Computer Modeling in Engineering and Sciences, 135, 2065-2089. https://doi.org/10.32604/cmes.2023.023408
• Alotaibi, R., Rezk, H., Park, C., Elshahhat, A. (2023). The discrete exponentiated-chen model and its applications. Symmetry, 15(6), 1278. https://doi.org/10.3390/sym15061278
• Arenas, J.M., Narbón, J.J., Alía, C. (2010). Optimum adhesive thickness in structural adhesives joints using statistical techniques based on Weibull distribution. International Journal of Adhesion and Adhesives, 30(3), 160-165. https://doi.org/10.1016/j.ijadhadh.2009.12.003
• Arshad, M.Z., Iqbal, M.Z., Ahmad, M. (2020). Exponentiated distribution: Properties and applications. Journal of Statistical Theory and Applications, 19(2), 297-313. https://doi.org/10.2991/jsta.d.200514.001
• Ashour, S.K., Eltehiwy, M.A. (2015). Exponentiated power Lindley distribution. Journal of advanced research, 6(6), 895-905. https://doi.org/10.1016/j.jare.2014.08.005
• Aslam, M., Azam, M., Balamurali, S., Jun, C.H. (2015). An economic design of a group sampling plan for a Weibull distribution using a Bayesian approach. Journal of Testing and Evaluation, 43(6), 1497-1503. https://doi.org/10.1520/JTE20140041
• Barman, A., Chakraborty, A.K., Goswami, A., Banerjee, P., De, P.K. (2023). Pricing and inventory decision in a two-layer supply chain under the weibull distribution product deterioration: An application of NSGA-II. RAIRO-Operations Research, 57(4), 2279-2300. https://doi.org/10.1051/ro/2023105
• Carrasco, J.M., Ortega, E.M., Cordeiro, G.M. (2008). A generalized modified Weibull distribution for lifetime modeling. Computational Statistics and Data Analysis, 53(2), 450-462. https://doi.org/10.1016/j.csda.2008.08.023
• Cordeiro, G.M., de Castro, M. (2011). A new family of generalized distributions. Journal of statistical computation and simulation, 81(7), 883-898. https://doi.org/10.1080/00949650903530745
• Cordeiro, G.M., Alizadeh, M., Ortega, E.M. (2014). The exponentiated half-logistic family of distributions: Properties and applications. Journal of Probability and Statistics, 2014. https://doi.org/10.1155/2014/864396
• Dokur, E., Kurban, M. (2015). Wind speed potential analysis based on Weibull distribution. Balkan Journal of Electrical and Computer Engineering, 3(4), 231 - 235. https://doi.org/10.17694/bajece.72748
• Dombi, J., Jonas, T., Toth, Z.E., Arva, G. (2019). The omega probability distribution and its applications in reliability theory. Quality and Reliability Engineering International, 35(2), 600-626. https://doi.org/10.1002/qre.2425
• El-Monsef, M.M., Sweilam, N.H., Sabry, M.A. (2021). The exponentiated power Lomax distribution and its applications. Quality and Reliability Engineering International, 37(3), 1035-1058. https://doi.org/10.1002/qre.2780
• Feroze, N., Tahir, U., Noor-ul-Amin, M., Nisar, K.S., Alqahtani, M.S., Abbas, M., Ali, R., Jirawattanapanit, A. (2022). Applicability of modified weibull extension distribution in modeling censored medical datasets: a bayesian perspective. Scientific Reports, 12(1), 17157. https://doi.org/10.1038/s41598-022-21326-w
• Genç, M., Özbilen, Ö. (2023). An extension of the UEHL distribution based on the DUS transformation. Journal of New Theory, 44, 20-30. https://doi.org/10.53570/jnt.1317652
• Gradshteyn, I.S., Ryzhik, I.M. (2007). Table of integrals, series, and products (7th edition ed.). San Diego: Academic press.
• Ghazal, M.G.M., Radwan, H.M.M. (2022). A reduced distribution of the modified Weibull distribution and its applications to medical and engineering data. Mathematical Biosciences and Engineering, 19(12), 13193-13213. https://doi.org/10.3934/mbe.2022617
• Gui, W. (2017). Exponentiated half logistic distribution: Different estimation methods and joint confidence regions. Communications in Statistics-Simulation and Computation, 46(6), 4600-4617. https://doi.org/10.1080/03610918.2015.1122053
• Gupta, R.C., Gupta, P.L., Gupta, R.D. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory and Methods, 27(4), 887-904. https://doi.org/10.1080/03610929808832134
• Ijaz, M., Asim, S.M., Alamgir, Farooq, M., Khan, S.A., Manzoor, S. (2020). A Gull Alpha Power Weibull distribution with applications to real and simulated data. Plos One, 15(6), e0233080. https://doi.org/10.1371/journal.pone.0233080
• Kang, S-B., Jung-In S., (2011). Estimation in an exponentiated half logistic distribution under progressively type-II censoring. Communications for Statistical Applications and Methods, 18(5), 657-666. https://doi.org/10.5351/CKSS.2011.18.5.657
• Khalil, A., Ijaz, M., Ali, K., Mashwani, W.K., Shafiq, M., Kumam, P., Kumam, W. (2021). A novel flexible additive Weibull distribution with real-life applications. Communications in Statistics-Theory and Methods, 50(7), 1557-1572. https://doi.org/10.1080/03610926.2020.1732658
• Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2), 79-88. https://doi.org/10.1016/0022-1694(80)90036-0
• Kundu, D., Raqab, M.Z. (2005). Generalized Rayleigh distribution: Different methods of estimation. Computational statistics and data analysis, 49(1), 187-200. https://doi.org/10.1016/j.csda.2004.05.008
• Lai, C.D. (2014). Generalized Weibull Distributions. Springer, ISBN: 978-3-642-39105-7, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39106-4
• Lehmann, E.L. (1953). The power of rank tests. The Annals of Mathematical Statistics, 24(1), 23-43. https://doi.org/10.1214/aoms/1177729080
• McCool, J.I. (2012). Using the Weibull Distribution: Reliability, Modeling, and Inference. John Wiley and Sons, ISBN:9781118217986, New Jersey. https://doi.org/10.1002/9781118351994
• Mudholkar, G.S., Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42, 299-302. https://doi.org/10.1109/24.229504
• Mudholkar, G.S., Srivastava, D.K., Freimer, M. (1995) The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics, 37, 436-445. https://doi.org/10.1080/00401706.1995.10484376
• Murthy, D.P., Xie, M., Jiang, R. (2004). Weibull Models. John Wiley and Sons, ISBN: 978-0-471-47327-5, Hoboken, New Jersey.
• Nadar, M., Papadopoulos, A., Kızılaslan, F. (2013). Statistical analysis for Kumaraswamy’s distribution based on record data. Statistical Papers, 54, 355-369. https://doi.org/10.1007/s00362-012-0432-7
• Özbilen, Ö., Genç, A.İ. (2022). A bivariate extension of the omega distribution for two-dimensional proportional data. Mathematica Slovaca, 72(6), 1605-1622. https://doi.org/10.1515/ms-2022-0111
• Periyasamypandian, J., Balamurali, S. (2023). Determination of new multiple deferred state sampling plan with economic perspective under Weibull distribution. Journal of Applied Statistics, 50(13), 2796-2816. https://doi.org/10.1080/02664763.2022.2091526
• Rastogi, M.K. (2014). Parameter and reliability estimation for an exponentiated half-logistic distribution under progressive type II censoring. Journal of Statistical Computation and Simulation, 84(8), 1711-1727. https://doi.org/10.1080/00949655.2012.762366
• Rather, A.A., Subramanian, C., Al-Omari, A.I., Alanzi, A.R. (2022). Exponentiated Ailamujia distribution with statistical inference and applications of medical data. Journal of Statistics and Management Systems, 25(4), 907-925. https://doi.org/10.1080/09720510.2021.1966206
• Rehman, H., Chandra, N., Hosseini-Baharanchi, F.S., Baghestani, A.R., Pourhoseingholi, M. A. (2022). Cause-specific hazard regression estimation for modified Weibull distribution under a class of non-informative priors. Journal of Applied Statistics, 49(7), 1784-1801. https://doi.org/10.1080/02664763.2021.1882407
• Seo, J.I., Kang, S.B. (2015). Notes on the exponentiated half logistic distribution. Applied Mathematical Modelling, 39(21), 6491-6500. https://doi.org/10.1016/j.apm.2015.01.039
• Sharma, V.K., Singh, S.V., Shekhawat, K. (2022). Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions. Journal of Applied Statistics, 49(2), 371-393. https://doi.org/10.1080/02664763.2020.1813694
• Surles, J., Padgett, W. (2001). Inference for reliability and stress-strength for a scaled Burr type X distribution. Lifetime data analysis, 7, 187-200. https://doi.org/10.1023/A:1011352923990
• Sürücü, B., Sazak, H.S. (2009). Monitoring reliability for a three-parameter Weibull distribution. Reliability Engineering & System Safety, 94(2), 503-508. https://doi.org/10.1016/j.ress.2008.06.001