Statistical Inference of Exponential Record Data Under Kullback-Leibler Divergence Measure

• Autorzy: Raed R. Abu Awwad , Ghassan K. Abufoudeh , Omar M. Bdair
• Języki publikacji: EN

Abstrakty

EN

Based on one parameter exponential record data, we conduct statistical inferences (maximum likelihood estimator and Bayesian estimator) for the suggested model parameter. Our second aim is to predict the future (unobserved) records and to construct their corresponding prediction intervals based on observed set of records. In the estimation and prediction processes, we consider the square error loss and the Kullback-Leibler loss functions. Numerical simulations were conducted to evaluate the Bayesian point predictor for the future records. Finally, data analyses involving the times (in minutes) to breakdown of an insulating fluid between electrodes at voltage 34 kv have been performed to show the performance of the methods thus developed on estimation and prediction. (original abstract)

Słowa kluczowe

EN

Bayesian estimation; Bayesian inference; Divergence

PL

Estymacja bayesowska; Wnioskowanie bayesowskie; Dywergencja

• Czasopismo: Statistics in Transition
• Rocznik: 2019
• Tom: 20
• Numer: nr 2
• Strony: 1--14

Twórcy

autor

Raed R. Abu Awwad

• University of Petra, Amman, Jordan

autor

Ghassan K. Abufoudeh

• University of Petra, Amman, Jordan

autor

Omar M. Bdair

• Al-Balqa Applied University, Amman, Jordan

Bibliografia

• ABUFOUDEH, G., BDAIR, O. M., ABU AWWAD, R., (2019). Bayesian Estimation Under Kullback-Leibler Divergence Measure Based on Exponential Data, Investigacion Operacional, 40 (1), pp. 61-72.
• AHSANULLAH, M. (1980). Linear Prediction of Record Values for the Two Parameter Exponential Distribution, Annals of the Institute of Statistical Mathematics, 32, pp. 363-368.
• AHSANULLAH, M., (1988). Introduction to Record Statistics, Ginn Press, Needham Heights, MA, U.S.A.
• AHSANULLAH, M., (1995). Record Statistics, Nova Science Publishers, Commack, NY.
• AHSANULLAH, M., KIRMANI, S., (1991). Characterizations of the Exponential Distribution Through a Lower Records, Communications in Statistics - Theory and Methods, 20, pp. 1293-1299.
• ARNOLD, B. C., BALAKRISHNAN, N., (1989). Relations, Bounds and Approximations for Order Statistics, Lecture Notes in Statistics, 53, Springer-Verlag, New York.
• ARNOLD, B. C., BALAKRISHNAN, N., NAGARAJA, H. N., (1998). Records, Wiley, New York.
• BALAKRISHNAN, N., AHSANULLAH, M., CHAN, P.S., (1995). On the Logistic Record Values and Associated Inference, Journal of Applied Statistical Science, 2, pp. 233-248.
• BALAKRISHNAN, N., LIN, C. T., CHAN, P.S., (2005). A Comparison of Two Simple Prediction Intervals for Exponential Distribution, IEEE T. Reliab., 54 (1), pp. 27-33.
• BDAIR, O. M., RAQAB, M. Z., (2009). On the Mean Residual Waiting Time of Records, Statistics and Decisions, 27 (3), pp. 249-260.
• BDAIR, O. M., RAQAB, M. Z., (2012). Sharp Upper Bounds for the Mean Residual Waiting Time of Records, Statistics, 46 (1), pp. 69-84.
• BDAIR, O. M., RAQAB, M. Z., (2016). One-Sequence and Two-Sequence Prediction for Future Weibull Records, J. Stat. Theory Appl., 15 (4), pp. 345-366.
• BERRED, A. M., (1998). Prediction of Record Values, Communications in Statistics - Theory and Methods, 27, 2221-2240.
• CHANDLER, K.N., (1952). The Distribution and Frequency of Record Values, Journal of the Royal Statistical Society - Series B, 14 (2), pp. 220-228.
• DUNSMORE, I. R., (1983). The Future Occurrence of Records, Ann. Inst. Statist. Math., 35, pp. 267-277.
• JANEEN, Z.F., (2004). Empirical Bayes Analysis of Record Statistics Based on LINEX and Quadratic Loss Functions, Comput. Math. Appl., 47, pp. 947- 954.
• KAMPS, U., (1995). A Concept of Generalized Order Statistics, J. Statist. Plan. Inference, 48, 1-23.
• KULLBACK, S., LEIBLER, R.A. (1951). On Information and Sufficiency, Annals of Mathematical Statistics, 22(1), pp. 79-86.
• LAWLESS, J. F., (1982). Statistical Models and Methods for Lifetime Data, 2nd Edition, Wiley, New York.
• NASIRI, P., HOSSEINI, S., YARMOHAMMADI, M., (2012). A New Approach to Statistical Inference for Exponential Distribution Based on Record Values, Canadian Journal of Pure and Applied Sciences, 6, pp. 2033-2038.
• NEVZOROV, V. B., (2001). Records: Mathematical Theory. Translations of Mathematical Monographs, American Mathematical Society, 194: Providence, RI.
• SINGH, S., SINGH, U., SHARMA, V., (2014). Bayesian Estimation and Prediction for the Generalized Lindley Distribution Under Asymmetric Loss Function, Hacettepe Journal of Mathematics and Statistics, 43 (4), pp. 661-678.

Identyfikatory

DOI

10.21307/stattrans-2019-011