Prediction of <Emphasis Type="Italic">k</Emphasis>-records from a general class of distributions under balanced type loss functions |
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Authors: | Jafar Ahmadi Mohammad Jafari Jozani Éric Marchand Ahmad Parsian |
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Institution: | (1) School of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 91775-1159, Mashhad, Iran;(2) Department of Statistics, Faculty of Economics, Statistical Research and Training Center (SRTC), Allameh Tabatabaie University, Tehran, Iran;(3) Département de mathématiques, Université de Sherbrooke, Sherbrooke, QC, Canada, J1K 2R1;(4) School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran |
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Abstract: | We study the problem of predicting future k-records based on k-record data for a large class of distributions, which includes several well-known distributions such as: Exponential, Weibull
(one parameter), Pareto, Burr type XII, among others. With both Bayesian and non-Bayesian approaches being investigated here,
we pay more attention to Bayesian predictors under balanced type loss functions as introduced by Jafari Jozani et al. (Stat
Probab Lett 76:773–780, 2006a). The results are presented under the balanced versions of some well-known loss functions, namely
squared error loss, Varian’s linear-exponential loss and absolute error loss or L
1 loss functions. Some of the previous results in the literatures such as Ahmadi et al. (Commun Stat Theory Methods 34:795–805,
2005), and Raqab et al. (Statistics 41:105–108, 2007) can be achieved as special cases of our results.
Partial support from Ordered and Spatial Data Center of Excellence of Ferdowsi University of Mashhad is acknowledged by J.
Ahmadi. M. J. Jozani’s research supported partially by a grant of Statistical Research and Training Center. é. Marchand’s
research supported by NSERC of Canada. A. Parsian’s research supported by a grant of the Research Council of the University
of Tehran. |
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Keywords: | Absolute value error loss Balanced loss function Bayes prediction Conditional median prediction Maximum likelihood prediction LINEX loss Record values |
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