بعض خصائص توزيع جمبيرتز توب ليون معكوس ويبل مع تطبيق
محتوى المقالة الرئيسي
الملخص
في هذا البحث سنقدم توزيعا جديدا يتكون من اربعة معالم ويسمى بتوزيع جمبيرتز توب ليون معكوس ويبل وتمتاز بمرونة عالية وملائمة جيدة لنمذجة البيانات. كما ويمكن دمج معكوس التوزيع ويبل بمعالم أكثر لتوليد العديد من التوزيعات الجديدة. ثم نقوم بتوسيع التوزيع وإعادة كتابة كل من دالة التوزيع التراكمي CDF ودالة الكثافة الاحتمالية PDF لتوزيع جديد وايضا يعطي التوزيع الجديد اشكال بيانية لدالة الكثافة الاحتمالية وتكون ممتدة أكثر او الملتوية لليسار. كما نقدم العديد من الخصائص الاحصائية للتوزيع الجديد مثل العزوم والدالة المولدة للعزوم والدالة التجزيئية والدالة البقاء ودالة المخاطرة وبعض الدوال الاخرى. وكذلك تم تطبيق طريقة الامكان الاعظم لتقدير معالم التوزيع الجديد. ولبيان مدى ملائمة ومرونة التوزيع الجديد تم استخدام مجموعة من البيانات الحقيقية التي تتعلق بأجمالي انتاج حليب في اول ولادة (107) بقرة من سلالة SINDI وحيث اثبت التوزيع الجديد ملائمة عالية ومرونة جيدة في نمذجة للبيانات الحقيقية بالمقارنة مع بعض التوزيعات المعروفة باستخدام بعض المعايير الاحصائية.
التنزيلات
تفاصيل المقالة
المراجع
Abdullah, Z. M., Hussain, N. K., Fawzi, F. A., Abdal-Hammed, M. K., & Khaleel, M. A., (2022), Estimating parameters of Marshall Olkin Topp Leon exponential distribution via grey wolf optimization and conjugate gradient with application. International Journal of Nonlinear Analysis and Applications, 13(1), 3491-3503.
Abid, S. H., & Abdulrazak, R. K., (2017), truncated Fréchet-gamma and inverted gamma distributions. International Journal of Scientific World, 5(2), 151-167. DOI: https://doi.org/10.14419/ijsw.v5i2.8363
Afify, A. Z., Ahmed, S., & Nassar, M., (2021), A new inverse Weibull distribution: properties, classical and Bayesian estimation with applications. Kuwait Journal of Science, 48(3). DOI: https://doi.org/10.48129/kjs.v48i3.9896
Ahmed, M. T., Khaleel, M. A., & Khalaf, E. K., (2020), The new distribution (Topp Leone Marshall Olkin-Weibull) properties with an application. Periodicals of Engineering and Natural Sciences, 8(2), 684-692.
Ahmed, M. T., Khaleel, M. A., Oguntunde, P. E., & Abdel-Hammed, M. K., (2021), March). A new version of the exponentiated Burr X distribution. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012116). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1818/1/012116
Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B., & Ghosh, I., (2017), The Gompertz-G family of distributions. Journal of statistical theory and practice, 11, 179-207. DOI: https://doi.org/10.1080/15598608.2016.1267668
Al-Noor, N. H., & Khaleel, M. A., (2021, March), Marshal Olkin Marshal Olkin Gompertz distribution. In AIP Conference Proceedings (Vol. 2334, No. 1, p. 090001). AIP Publishing LLC. DOI: https://doi.org/10.1063/5.0042235
Al-Noor, N. H., Khaleel, M. A., & Assi, N. K., (2022), The Rayleigh Gompertz distribution: Theory and real applications. International Journal of Nonlinear Analysis and Applications, 13(1), 3505-3516.
Al-Noor, N. H., Khaleel, M. A., & Mohammed, G. J., (2021, September), Theory and applications of Marshall Olkin Marshall Olkin Weibull distribution. In Journal of Physics: Conference Series (Vol. 1999, No. 1, p. 012101). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1999/1/012101
Bera, W. T., (2015), The Kumaraswamy inverse Weibull Poisson distribution with applications. Indiana University of Pennsylvania.
Bourguignon, M., Silva, R. B., & Cordeiro, G. M., (2014), The Weibull-G family of probability distributions. Journal of data science, 12(1), 53-68. DOI: https://doi.org/10.6339/JDS.201401_12(1).0004
Chipepa, F., & Oluyede, B., (2021), The Marshall-Olkin-Gompertz-G family of distributions: properties and applications. J. Nonlinear Sci. Appl, 14(4), 257-260. DOI: https://doi.org/10.22436/jnsa.014.04.05
Eugene, N., Lee, C., & Famoye, F., (2002), Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31(4), 497-512. DOI: https://doi.org/10.1081/STA-120003130
Hassan, A. S., Almetwally, E. M., Khaleel, M. A., & Nagy, H. F., (2021), Weighted power Lomax distribution and its length biased version: Properties and estimation based on censored samples. Pakistan Journal of Statistics and Operation Research, 343-356. DOI: https://doi.org/10.18187/pjsor.v17i2.3360
Ibrahim, N. A., Khaleel, M. A., Merovci, F., Kilicman, A., & Shitan, M., (2017), Weibull Burr X Distribution Properties and Application. Pakistan Journal of Statistics, 33(5).
Khaleel, M. A., Abdulwahab, A. M., Gaftan, A. M., & Abdel-hammed, M. K., (2022), A new [0, 1] truncated inverse Weibull Rayleigh distribution properties with application to COVID-19. International Journal of Nonlinear Analysis and Applications, 13(1), 2933-2946.
Khaleel, M. A., Al-Noor, N. H., & Abdal-Hameed, M. K., (2020), Marshall Olkin exponential Gompertz distribution: Properties and applications. Periodicals of Engineering and Natural Sciences, 8(1), 298-312.
Khaleel, M. A., Ibrahim, N. A., Shitan, M., & Merovci, F., (2016, June), Some properties of Gamma Burr type X distribution with application. In AIP Conference proceedings (Vol. 1739, No. 1, p. 020087). AIP Publishing LLC. DOI: https://doi.org/10.1063/1.4952567
Khaleel, M. A., Ibrahim, N. A., Shitan, M., Merovci, F., & Rehman, E., (2017), Beta burr type x with application to rainfall data. Malaysian Journal of Mathematical Sciences, 11, 73-86.
Khaleel, M. A., Oguntunde, P. E., Ahmed, M. T., Ibrahim, N. A., & Loh, Y. F., (2020), The Gompertz flexible Weibull distribution and its applications. Malaysian Journal of Mathematical Sciences, 14(1), 169-190.
Khaleel, M. A., Oguntunde, P. E., Al Abbasi, J. N., Ibrahim, N. A., & AbuJarad, M. H. (2020). The Marshall-Olkin Topp Leone-G family of distributions: A family for generalizing probability models. Scientific African, 8, e00470.
Khaleel, M. A., Oguntunde, P. E., Al Abbasi, J. N., Ibrahim, N. A., & AbuJarad, M. H., (2020), The Marshall-Olkin Topp Leone-G family of distributions: A family for generalizing probability models. Scientific African, 8, e00470. DOI: https://doi.org/10.1016/j.sciaf.2020.e00470
Khan, M. S., & King, R., (2012), Modified inverse Weibull distribution. Journal of statistics applications & Probability, 1(2), 115. DOI: https://doi.org/10.12785/jsap/010204
Khan, M. S., Pasha, G. R., & Pasha, A. H., (2008), Theoretical analysis of inverse Weibull distribution. WSEAS Transactions on Mathematics, 7(2), 30-38.
Kundu, D., & Howlader, H., (2010), Bayesian inference and prediction of the inverse Weibull distribution for Type−II censored data. Computational Statistics & Data Analysis, 54(6), 1547-1558. DOI: https://doi.org/10.1016/j.csda.2010.01.003
Maxwell, O., Chukwu, A. U., Oyamakin, O. S., & Khaleel, M. A., (2019), The Marshall-Olkin inverse Lomax distribution (MO-ILD) with application on cancer stem cell. Journal of Advances in Mathematics and Computer Science, 33(4), 1-12. DOI: https://doi.org/10.9734/jamcs/2019/v33i430186
Merovci, F., Khaleel, M. A., Ibrahim, N. A., & Shitan, M., (2016), The beta Burr type X distribution properties with application. Springer Plus, 5, 1-18. DOI: https://doi.org/10.1186/s40064-016-2271-9
Mudholkar, G. S., & Kollia, G. D., (1994), Generalized Weibull family: a structural analysis. Communications in statistics-theory and methods, 23(4), 1149-1171. DOI: https://doi.org/10.1080/03610929408831309
Muhammed, H. Z., & Almetwally, E. M., (2020), Bayesian and non-Bayesian estimation for the bivariate inverse Weibull distribution under progressive type-II censoring. Annals of Data Science, 1-32. DOI: https://doi.org/10.1007/s40745-020-00316-7
Oguntunde, P. E., Khaleel, M. A., Adejumo, A. O., & Okagbue, H. I., (2018), A study of an extension of the exponential distribution using logistic-x family of distributions. International Journal of Engineering and Technology, 7(4), 5467-5471.
Oguntunde, P. E., Khaleel, M. A., Ahmed, M. T., Adejumo, A. O., & Odetunmibi, O. A., (2017), A new generalization of the Lomax distribution with increasing, decreasing, and constant failure rate. Modelling and Simulation in Engineering, 2017. DOI: https://doi.org/10.1155/2017/6043169
Rannona, K., Oluyede, B., & Chamunorwa, S., (2022), The Gompertz-Topp Leone-G Family of Distributions with Applications. Journal of Probability and Statistical Science, 20(1), 108-126. DOI: https://doi.org/10.37119/jpss2022.v20i1.630
Yousof, H. M., Alizadeh, M., Jahan Shahi, S. M. A., Ghosh, T. G. R. I., & Hamedani, G. G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications. Journal of Data Science, 15(4), 723-740. DOI: https://doi.org/10.6339/JDS.201710_15(4).00008