An Extended UEHL Distribution: Properties and Applications

Yıl 2024, Cilt: 20 Sayı: 2, 37 - 44, 28.06.2024

Murat Genç , Ömer Özbilen

https://doi.org/10.18466/cbayarfbe.1435139

Öz

This study introduces a new distribution, a Lehmann-type exponentiated distribution, which is built upon the unit exponentiated half-logistic distribution. The analytical characteristics of the proposed distribution, like moments, moment-generating function, quantiles, and stress-strength reliability, are explored in detail. The renowned maximum likelihood estimation method is employed for the statistical inference of the distribution’s parameters. A computer experiment is run to explore the performance of the maximum likelihood estimates of the distribution parameters under diverse scenarios. Additionally, the practicality and efficacy of the distribution are illustrated through a numerical example using a real-world dataset.

Anahtar Kelimeler

Exponentiated family, G-family, Maximum likelihood estimator, Reliability, UEHL distribution

Kaynakça

• [1]. Al-Babtain, AA, Elbatal, I, Chesneau, C, Elgarhy, M. 2020. Sine Topp-Leone-G family of distributions: Theory and applications. Open Physics; 18(1): 574-593.
• [2]. Hussein, M, Cordeiro, GM, De Santana, LH, Rodrigues, GM, Ortega, EM. 2022. Odd Pareto-G Family: Properties, Regression, Simulations and Applications. Contemporary Mathematics; 4(1): 49-74.
• [3]. Gabanakgosi, M, Oluyede, B. 2023. The Topp-Leone type II exponentiated half logistic-G family of distributions with applications. International Journal of Mathematics in Operational Research; 25(1): 85-117.
• [4]. Carrasco, JM, Ortega, EM, Cordeiro, GM. 2008. A generalized modified Weibull distribution for lifetime modeling. Computational Statistics & Data Analysis; 53(2): 450-462.
• [5]. Almalki, SJ, Nadarajah, S. 2014. Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety; 124: 32-55.
• [6]. Johnson, NL. 1949. Systems of frequency curves generated by methods of translation. Biometrika; 36: 149-176.
• [7]. Tadikamalla, PR, Johnson, NL, 1982. Systems of frequency curves generated by transformations of logistic variables, Biometrika; 69: 461-465.
• [8]. Korkmaz, MÇ. 2020. A new heavy-tailed distribution defined on the bounded interval: The logit slash distribution and its application, Journal of Applied Statistics; 47: 2097–2119.
• [9]. Gündüz, S, Korkmaz, MÇ. 2020. A new unit distribution based on the unbounded johnson distribution rule: The unit johnson su distribution, Pakistan Journal of Statistics and Operation Research; 16: 471-490.
• [10]. Altun, E, Hamedani, G. 2018. The log-xgamma distribution with inference and application, Journal of the French Statistical Society; 159: 40-55.
• [11]. Mazucheli, J, Menezes, AFB, Ghitany, ME. 2018. The unit-Weibull distribution and associated inference. Journal of Applied Probability and Statistics; 13(2): 1-22.
• [12]. Mazucheli, J, Menezes, AF, Dey, S. 2018. The unit-Birnbaum-Saunders distribution with applications. Chilean Journal of Statistics; 9(1): 47-57.
• [13]. Ghitany, ME, Mazucheli, J, Menezes, AFB, Alqallaf, F. 2019. The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval. Communications in Statistics-Theory and methods; 48(14): 3423-3438.
• [14]. Altun, E. 2021. The log-weighted exponential regression model: alternative to the beta regression model. Communications in Statistics-Theory and Methods; 50(10): 2306-2321.
• [15]. Sindhu, TN, Shafiq, A, Huassian, Z. 2024. Generalized exponentiated unit Gompertz distribution for modeling arthritic pain relief times data: classical approach to statistical inference. Journal of Biopharmaceutical Statistics; 34(3): 323-348.
• [16]. Dombi, J, Jonas, T, Toth, ZE, Arva, G. 2019. The omega probability distribution and its applications in reliability theory. Quality and Reliability Engineering International; 35(2): 600-626.
• [17]. Özbilen, Ö, Genç, Aİ. 2022. A bivariate extension of the omega distribution for two-dimensional proportional data. Mathematica Slovaca; 72(6): 1605-1622.
• [18]. Seo, JI, Kang, SB. 2015. Notes on the exponentiated half logistic distribution. Applied Mathematical Modelling; 39(21): 6491-6500.
• [19]. Gui, W. 2017. Exponentiated half logistic distribution: Different estimation methods and joint confidence regions. Communications in Statistics-Simulation and Computation; 46(6): 4600-4617.
• [20]. Kang, SB, Seo, JI. 2011. Estimation in an Exponentiated Half Logistic Distribution under Progressively Type-2 Censoring. Communications for Statistical Applications and Methods; 18(5): 657-666.
• [21]. Rastogi, MK, Tripathi, YM. 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.
• [22]. Ali, MM, Ali, I, Yousof, HM, Ahmed, MIM. 2023. G Families of Probability Distributions: Theory and Practices. CRC Press.
• [23]. Tahir, MH, Nadarajah, S. 2015. Parameter induction in continuous univariate distributions: Well-established G families. Anais da Academia Brasileira de Ciências; 87: 539-568.
• [24]. Bourguignon, M, Silva, RB, Cordeiro, GM. 2014. The Weibull-G family of probability distributions. Journal of Data Science; 12(1): 53-68.
• [25]. Shukla, AK, Soni, S, Kumar, K. 2023. An inferential analysis for the Weibull-G family of distributions under progressively censored data. OPSEARCH; 60: 1488-1524.
• [26]. Tahir, M, Zubair, M, Mansoor, M, Cordeiro, GM, Alizadehk M, GG, H. 2016. A new Weibull-G family of distributions. Hacettepe Journal of Mathematics and statistics; 45(2): 629-647.
• [27]. Korkmaz, MÇ. 2018. A new family of the continuous distributions: the extended Weibull-G family. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics; 68(1): 248-270.
• [28]. Alizadeh, M, Cordeiro, GM, Pinho, LGB, Ghosh, I. 2017. The Gompertz-G family of distributions. Journal of statistical theory and practice; 11: 179-207.
• [29]. Badr, MM, Elbatal, I, Jamal, F, Chesneau, C, Elgarhy, M. 2020. The transmuted odd Fréchet-G family of distributions: Theory and applications. Mathematics; 8(6): 958.
• [30]. Ul Haq, MA, Elgarhy, M. 2018. The Odd Frѐchet-G family of probability distributions. Journal of Statistics Applications & Probability; 7(1): 189-203.
• [31]. Eghwerido, JT, Efe-Eyefia, E, Zelibe, SC. 2021. The transmuted alpha power-G family of distributions. Journal of Statistics and Management Systems; 24(5): 965-1002.
• [32]. Chakraborty, S, Handique, L, Jamal, F. 2022. The Kumaraswamy Poisson-G family of distribution: its properties and applications. Annals of Data Science; 9(2): 229-247.
• [33]. Alnssyan, B, Hussein, EA, Alizadeh, M, Afify, AZ, Abdellatif, AD. 2023. The weighted Lindley-G family of probabilistic models: properties, inference, and applications to real-life data. Journal of Intelligent & Fuzzy Systems; 44(5): 8071-8089.
• [34]. Mazucheli, J, Menezes, AFB, Fernandes, LB, De Oliveira, RP, Ghitany, ME. 2020. The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics; 47(6): 954-974.
• [35]. Kumaraswamy, P. 1980. A generalized probability density function for double-bounded random processes. Journal of hydrology; 46(1-2): 79-88.
• [36]. Guerra, RR, Peña-Ramírez, FA, Bourguignon, M. 2021. The unit extended Weibull families of distributions and its applications. Journal of Applied Statistics; 48(16): 3174-3192.
• [37]. Chakraborty, S, Ong, SH, Ng, CM. 2023. A new probability model with support on unit interval: Structural properties, regression of bounded response and applications. Journal of Statistical Theory and Practice; 17(4): 1-32.
• [38]. Masood, B, Bashir, S, Masood, N. 2023. Unit Interval Exponentiated Exponential Distribution and Quantile Regression Model: Applications for the COVID-19 Data and Bounded Responses Data. Annals of Human and Social Sciences; 4(4): 51-66.
• [39]. Korkmaz, MÇ, Korkmaz, ZS. 2023. The unit log–log distribution: A new unit distribution with alternative quantile regression modeling and educational measurements applications. Journal of Applied Statistics; 50(4): 889-908.
• [40]. Akata, IU, Opone FC, Osagiede, FEU. 2023. The Kumaraswamy Unit-Gompertz Distribution and its Application to Lifetime Datasets. Earthline Journal of Mathematical Sciences; 11(1): 1-22.
• [41]. Genç, M, Özbilen, Ö. 2023. An Extension of the UEHL Distribution Based on the DUS Transformation. Journal of New Theory; 44: 20-30.
• [42]. Genç, M, Özbilen, Ö. 2023. Exponentiated UEHL Distribution: Properties and Applications. Recep Tayyip Erdoğan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi; 4(2): 232-241.
• [43]. Nadarajah, S. 2005. Exponentiated beta distributions. Computers & Mathematics with Applications; 49(7-8): 1029-1035.
• [44]. Gradshteyn, IS, Ryzhik, IM. 2007. Table of integrals, series, and products, 7th edition dü.. San Diego: Academic press.
• [45]. Dumonceaux, R, Antle, CE. 1973. Discrimination between the log-normal and the Weibull distributions. Technometrics; 15(3): 923-926.
• [46]. Bantan, RAR, Chesneau, C, Jamal, F, Elgarhy, M, Almutiry, W, Alahmadi, AA. 2021. Study of a Modified Kumaraswamy Distribution. Mathematics; 9(21): 2836.