Based on record statistics from Lindley distribution, we consider here the problem of estimating the model parameter and predicting the unobserved records. Frequentist and Bayesian analyses are discussed for making some inferences for the model parameter and prediction of unobserved records. Frequentist methods involving maximum likelihood estimation and moments based estimation and Bayesian sampling-based technique are applied for estimating the unknown shape parameter as well as predicting the future unobserved units. The corresponding point predictors and credible intervals of future record values based on an informative set of records can be developed. Real data analysis has been performed for illustrative purposes.
A new extension of exponential distribution, called NH distribution, was recently introduced by Nadarajah and Haghighi (Statistics 45:543-558, 2011). In this paper, we consider the upper record values from this distribution. We obtain exact explicit expressions as well as several recurrence relations for the single and product moments of record values and then we use these results to compute the means, variances and the covariances of the upper record values. We make use of these calculated moments to find the best linear unbiased estimators (BLUEs) of the location and scale parameters of NH distribution. In addition, based on the observed records, we investigate how to obtain best linear unbiased predictor for the future record values. Confidence intervals for the unknown parameters and prediction intervals for future records are also discussed. Finally, we present an example in order to illustrate the inferential results obtained in this paper and compare the BLUEs with maximum likelihood estimators numerically.
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