Model Assisted Statistics and Applications 12 (2017) 15–29 15 DOI 10.3233/MAS-160380 IOS Press Statistical inference for the generalized Rayleigh distribution based on upper record values Sanku Dey a , Tanujit Dey b,∗ and Daniel Luckett c a Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India b Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, OH, USA c Department of Biostatistics, University of North Carolina at Chapel Hill, NC, USA Abstract. We consider the problem of estimating the parameters of generalized Rayleigh distribution both from frequentist and Bayesian point of view when the available data is in the form of record values. Bayes’ estimators of the unknown parameters are obtained under symmetric and asymmetric loss functions using gamma priors on both the shape and the scale parameters. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. We have also derived the Bayes intervals of the parameters and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values. Monte Carlo simulations are performed to compare the performances of the proposed methods, and one data set has been analyzed for illustrative purposes. Keywords: Bayes estimator, Bayes prediction, general entropy loss function, maximum likelihood estimator, median prediction JEL codes: 62C10, 62F10, 62F15, 65C10 1. Introduction Record values are used in many statistical applications, statistical modeling and inference involving data pertain- ing to weather, athletic events, economics, life testing studies and so on. For example, Guinness World Records, fastest time taken to recite the periodic table of the elements or shortest ever tennis matches both in terms of number of games and duration of time or fastest indoor marathon, etc. People make several attempts to make records but records are made only when the attempt is a success. Usually, we don’t get the data on all of the attempts made to break the records around the world. The data that we have are the records. Because of importance of record values in many fields of application, these kind of ordered data have been extensively studied in the literature. There are hundreds of papers and several books published on record-breaking data and its distributional properties (see, for instance, Chandler (1952), Resnick (1973), Shorrock (1973), Glick (1978), Nevzorov (1987), Ahsanullah (1995), Balakrishnan and Ahsanullah (1993), Arnold et al. (1998), Dey and Dey (2012), Dey et al. (2013) and Kumar (2015)). Hence, it is pertinent that one has accurate estimation procedures based on records. For formal definition of records, let {X i ,i  1} be a sequence of independent and identically distributed (iid) continuous random variables. An observation X j is called an upper record value if its value exceeds all previous * Corresponding author: Tanujit Dey, Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, OH, USA. E-mail: deyt@ccf. org. ISSN 1574-1699/17/$35.00 c  2017 – IOS Press and the authors. All rights reserved