Weibull modeline uygulamalar içeren genelleştirilmiş dağıtımların Libby-Novick beta sınıfı için yeni bir kapalı form.

Year 2021, , 23 - 42, 30.06.2021

Mohamed Ahmed

https://doi.org/10.52693/jsas.936902

Abstract

Matematiksel özelliklerin türetilmesinde, rastgele sayıların üretilmesinde ve gerçek veri setlerinin uygulanmasında daha iyi esneklik elde etmek için kapalı forma sahip olmayan sınıflar yerine basit bir kapalı forma sahip yeni dağıtım sınıfları türetmek yararlıdır. Bu makalede, değiştirilmiş Libby-Novick (MLN) sınıfı olarak adlandırılan genelleştirilmiş dağıtımların yeni bir kapalı form sınıfı, Libby-Novick beta sınıfının örtük formundan türetilmiştir. İki önemli dağıtım sınıfı, MLN sınıfı tarafından yuvalanmıştır. Bazı genelleştirilmiş matematiksel özellikler türetilmiş ve maksimum olabilirlik tahmini (MLE) yöntemi kullanılarak MLN sınıfı parametreleri tahmini elde edilmiştir. MLN-Weibull (MLN-W) dağılımının tahminci davranışını araştırmak için önyükleme yaklaşımını kullanan bir simülasyon çalışması uygulanmıştır. MLN-W'nin potansiyelini göstermek için gerçek bir veri seti kullanılır.

Keywords

yeni biçim Libby-Novick dağılımı, momentler, sıra istatistikleri, maksimum olasılık tahmini.

A new closed form for Libby-Novick beta class of generalized distributions with applications to Weibull model.

Abstract

It is useful to derive new classes of distributions having a simple closed form instead of classes having no closed form to get better flexibility in deriving mathematical properties, generating random numbers and applying real data sets. In this paper, a new closed form class of generalized distributions, so-called the modified Libby-Novick (MLN) class, is derived from the implicit form of Libby-Novick beta class. Two important classes of distributions are nested by the MLN class. Some generalized mathematical properties are derived and the MLN class parameters estimation using maximum likelihood estimation (MLE) method is obtained. A simulation study using bootstrapping approach is applied to investigate the estimators behavior of the MLN-Weibull (MLN-W) distribution. A real data set is used to illustrate the potentiality of the MLN-W

Keywords

the new form Libby-Novick distribution, moments, order statistics, maximum likelihood estimation.

References

• Ahmed, M.A. On the alpha power Kumaraswamy distribution: Properties, simulation and application. Revista Colombiana de Estadística. 2020; 43: 285-313.
• Ali Ahmed, M. The new form Libby-Novick distribution. Communications in Statistics-Theory and Methods. 2021; 50: 540-559.
• Arnold, CB, Balakrishnan, N, Nagaraja, HN. A first course in order statistics. John Wiley and Sons, Inc. New York; 1992.
• Alexander, C, Cordeiro, GM, Ortega, EMM, Sarabia JM. Generalized beta-generated distributions. Comput Stat Data Anal. 2012; 56: 1880-1897.
• Cordeiro, GM and de Castro, M. A New Family of Generalized Distributions. Journal of Statistical Computation & Simulation. 2011; 81: 883-898.
• Cordeiro, GM, de Santana, LH, Ortega, EM, Pescim, RR. A new family of distributions: Libby-Novick beta. International Journal of Statistics and Probability. 2014; 3: 63-80.
• Cordeiro, GM, Ortega, EMM , Nadarajah, S. The Kumaraswamy Weibull Distribution with Application to Failure Data. Journal of The Franklin Institute. 2010; 347:1399–1429.
• El-Sherpieny, EA and Ahmed, MA. On The Kumaraswamy Kumaraswamy Distribution. International Journal of Basic and Applied Sciences. 2014; 3: 372-381
• Eugene, N., Lee, C. and Famoye, F. Beta-Normal Distribution and Its Applications. Communications in Statistics, Theory and Methods. 2002; 31: 497-512.
• Garthwait, PH, Jolliffe, IP, jones, B. Statistical Inference. prentice Hall International (UK) Limited, London; 1995.
• Gradshteyn, IS, Ryzhik, IM. Tables of Integrals, Series, and Products. Academic Press, San Diego, CA; 2000.
• Greenwood, JA, Landwehr, JM, Matalas, NC, Wallis, JR. Probability Weighted Moments Definition and Relation to Parameters of Several Distributions. Expressable in Inverse Form. Water Resources Research.1979; 15: 1049-1054.
• Johnson, NL, Kotz, S, Balakrishnan, N. Continuous Univariate Distributions. John wiley and Sons, New York; 1995.
• Kumar, D. The Singh–Maddala distribution: properties and estimation. International journal of system assurance engineering and management. 2017; 8: 1297-1311.‏
• Kumaraswamy, P. Generalized Probability Density Function for Double-Bounded Random-Processes. Journal of Hydrology.1980; 46: 79-88.
• Libby, DL, Novick, MR. Multivariate generalized beta-distributions with applications to utility assessment. Journal of Educational Statistics.1982; 7: 271-294.
• Mahmoud, MR, El-Sherpieny, EA, Ahmed, MA. The New Kumaraswamy Kumaraswamy Family of Generalized Distributions with Application. Pakistan Journal of Statistics and Operations Research.2015; 11: 159-180.
• McDonald, JB. Some generalized functions for the size distribution of income. Econometrica.1984; 52: 647-664.
• Meeker, WQ and Escobar, LA. Statistical Methods for Reliability Data. John Wiley, New York; 1998.
• Merovcia, F and Puka, L.Transmuted Pareto Distribution. Prob Stat Forum. 2014; 7: 1-11.
• Prudnikov, AP, Brychkov, YA, Marichev, OI. Integrals and Series. Gordon and Breach Science Publishers, Amsterdam; 1986.
• Nassar, M.M., Eissa, F.H. On the exponentiated Weibull distribution. Communications in Statistics-Theory and Methods. 2003; 32: 1317-1336.
• Pescim, R. R., Cordeiro, G. M., Demétrio, C. G., Ortega, E. M., Nadarajah, S. The new class of Kummer beta generalized distributions. SORT-Statistics and Operations Research Transactions. 2012; 153-180.
• Wahed, AS. A General Method of Constructing Extended Families of Distribution from an Existing Continuous Class. Journal of Probability and Statistical Science. 2006; 4: 165-177.