Record values from NH distribution and associated inference.

*(English)*Zbl 1394.62059Summary: 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.

##### MSC:

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 |

##### Keywords:

best linear unbiased estimator; best linear unbiased predictor; incomplete gamma function; NH distribution; record values; recurrence relations; confidence intervals
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\textit{S. M. T. K. MirMostafaee} et al., Metron 74, No. 1, 37--59 (2016; Zbl 1394.62059)

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