Using the (Topp Leone G-Family) rule to build the probability distributions function
Keywords:
(Topp Leone), (Topp Leon G-family) (الامكان الاعظـم MLE), (المربعات الصغرى الموزونة (WLS), (طريقة التقليص Shrinkage) (Rayleigh Rayleigh distribution)Abstract
The (Topp Leone) distribution, the (Rayleigh) distribution. Are among the continuous distributions that are use in the analysis of survival and failure functions and reliability. This study used the (Topp Leone distribution) as a base for constructing a proposed probability distribution by adding a shape parameter to the (Expanding Rayleigh) distribution. It called (Topp Leon G-Rayleigh Rayleigh distribution (TLG-RR)). It is an extension and generalization of the (Rayleigh distribution).This study extracted some basic characteristics of the distribution, and estimate this distribution parameters and reliability function were estimated by three different estimation methods, such as (the greatest potential (MLE), weighted least squares (WLS) and the Shrinkage method. The study applied to real data for printer devices, and the study was able to prove that the proposed distribution (TLG-RR) is better in representing this data By using good conformance tests (AIC, AICc). And the best method for estimation is (shrinkage method), Depending on statistical criteria (Mse, IMse).
References
المصادر العربية:
- خميس، احمد جاسم، (2016) "مقدر بيز لدالة المعولية الضبابية لتوزيع رايأتي الاسي، باستعمال المحاكاة" مجلة كلية التربية، الإصدار: (5)، الصفحة: (318-289).
- مسلم باسم شليبة، كاظم اموري هادي، "القياس الاقتصادي المتقدم، النظرية والتطبيق" العراق، جامعة بغداد، مطبعة الطيف،2002، ص:107
- نصر الله، مهدي وهاب" بناء توزيع احتمالي اسي-باريتو الموزون مع تطبيق عملي" أطروحة دكتوراه في علم الإحصاء، كلية الإدارة والاقتصاد، جامعة بغداد،2015.
- نعيم، حيدر رسول، "تقدير دالة معوّليّة توزيع (Topp-Leone) مع تطبيق عملي"رسالة ماجستير، جامعة كربلاء، كلية الإدارة والاقتصاد،2021.
- هرمز، امير حنا، "الإحصاء الرياضي" دار الكتب للطباعة والنشر، 1990.ص:134-137.
المصادر الإنكليزية:
- Abushal, T. A., Hassan, A. S., El-Saeed, A. R., & Nassr, S. G. (2021) . Power inverted Topp–Leone distribution in acceptance sampling plans. Comput. Mater. Contin, 67, 991-1011.
- Aldahlan, M. A. (2019). Classical and Bayesian Estimation for Topp leone Inverse Rayleigh Distribution. Pure Mathematical Sciences, 8(1), 1-10.
- Ateeq, K., Qasim, T. B., & Alvi, A. R. (2019). An extension of Rayleigh distribution and applications. Cogent Mathematics & Statistics, 6(1), 1622191.
- Hassan, A. S., Elgarhy, M., & Ragab, R. (2020). Statistical properties and estimation of inverted Topp-Leone distribution. J. Stat. Appl. Probab, 9(2), 319
- Hendry, D. F., & Nielsen, B. (2007). Econometric modeling: a likelihood approach. Princeton University Press.
- Lehmann, E. L., & Casella, G. (2006). Theory of point estimation. Springer Science & Business Media.
- Rezaei, S., Sadr, B. B., Alizadeh, M., & Nadarajah, S. (2017). Topp–Leone generated family of distributions: Properties and applications. Communications in Statistics-Theory and Methods, 46(6), 2893-2909.
- Rossi, R. J. (2018). Mathematical statistics: an introduction to likelihood based inference. John Wiley & Sons.
- Sangsanit, Y., & Bodhisuwan, W. (2016). The Topp-Leone generator of distributions: properties and inferences. Songklanakarin Journal of Science & Technology, 38(5).
- Swain, J. J., Venkatraman, S., & Wilson, J. R. (1988). Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation, 29(4), 271-297.
- Thompson, J. R. (1968). Some shrinkage techniques for estimating the mean. Journal of the American Statistical Association, 63(321), 113-122.
- Topp, C. W., & Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269), 209-219.
- Yousof, H. M., Jahanshahi, S. M. A., Ramires, T. G., Aryal, G. R., & Hamedani, G. G. (2018). A NEW DISTRIBUTION FOR EXTREME VALUES: REGRESSION MODEL, CHARACTERIZATIONS AND APPLICATIONS. Journal of Data Science, 16(4).
المواقع الالكترونية
- http:// www.nid-moi.gov.iq.com.
- https://sites.google.com/site/learningandteachingstrategies1/lllllll/pp/ almhakate-wtmthyl-aladwar.com.
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