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Record values from NH distribution and associated inference. (English) Zbl 1394.62059
Summary: A new extension of exponential distribution, called NH distribution, was recently introduced by S. Nadarajah and F. Haghighi [Statistics 45, No. 6, 543–558 (2011; Zbl 1228.62018)]. 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.

62G30 Order statistics; empirical distribution functions
62E15 Exact distribution theory in statistics
62N02 Estimation in survival analysis and censored data
62E10 Characterization and structure theory of statistical distributions
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