Finally, a real data set is provided to illustrate the results.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:This paper deals with the statistical inference for the geometric process (GP), in which the time until the occurrence of the first event is assumed to follow inverse Rayleigh distribution.
📊
Key Findings & Data:The performances of the ML estimators are also compared with the corresponding non-parametric modified moment estimators in terms of bias, mean squared error and Pitman nearness probability through an extensive simulation study.
💡
Conclusion & Impact:Finally, a real data set is provided to illustrate the results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Geometric process · inverse Rayleigh distribution · maximum likelihood estimator
Abstract
This paper deals with the statistical inference for the geometric process (GP), in which the time until the occurrence of the first event is assumed to follow inverse Rayleigh distribution. The maximum likelihood (ML) method is used to derive the estimators of the parameters in GP. Asymptotic distributions of the ML estimators are obtained which help us to construct confidence intervals for the parameters and show the consistency of these estimators. The performances of the ML estimators are also compared with the corresponding non-parametric modified moment estimators in terms of bias, mean squared error and Pitman nearness probability through an extensive simulation study. Finally, a real data set is provided to illustrate the results.
USTA, İ. (2020). STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE INVERSE RAYLEIGH DISTRIBUTION. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 3, 871–882. https://ajindex.com/articles/419156
Cox D.R., Lewis P.A.W., (1966) The Statistical Analysis of Series of Events. Mathuen, London
Ascher H., Feingold H., (1984) Repairable Systems Reliability. Marcel Dekker, New York
Lam Y., (1988) A Note on the optimal replacement problem, Advances in Applied Probability 20, 479–482
Lam Y., (1988) Geometric process and replacement problem, Acta Mathematicae Applicatae Sinica 4, 366–377
Lam Y., (1992) Nonparametric inference for geometric process, Communications in Statistics – Theory and Methods 21, 2083– 2105
Lam Y., Zhu L.X., Chan J.S.K., Liu Q., (2004) Analysis of data from a series of events by a geometric process model, Acta Mathematicae Applicatae Sinica 20, 263–282
Lam Y., (2007) The Geometric Process and Its Applications. World Scientific, Singapore
Lam Y., Zheng Y.H., Zhang Y.L., (2003) Some limit theorems in geometric process, Acta Mathematicae Applicatae Sinica 19, 405–416
Braun W.J., Li W., Zhao Y.P., (2005) Properties of the geometric and related processes, Naval Research Logistic 52, 607–616
Lam Y., Chan S.K., (1998) Statistical inference for geometric processes with lognormal distribution, Computational Statistics and Data Analysis 27, 99–112
Chan S.K., Lam Y., Leung Y.P., (2004) Statistical inference for geometric processes with gamma distribution, Computational Statistics and Data Analysis 47, 565–581
Aydoğdu H., ¸Senoğlu B., Kara M., (2010) Parameter estimation in geometric process with Weibull distribution, Applied Mathematics and Computation 217, 2657–2665
Kara M., Aydoğdu H., Türkşen Ö. (2015) Statistical inference for geometric process with the inverse Gaussian distribution, Journal of Statistical Computation and Simulation 85, 3206–3215
Biçer C. (2018) Statistical inference for geometric process with the power Lindley distribution, Entropy 20, 723–743 [15] Biçer C., Biçer H.D., Kara M., Aydoğdu H. (2019) Statistical inference for geometric process with the Rayleigh distribution, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, 149–160
Voda, R. G., (1972). On the inverse Rayleigh variable, Reports of Statistical Application Research of the Union of Japanese Scientists and Engineers. 19, 15–21
Dey S. (2012) Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution, Malaysian Journal of Mathematical Scienc