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Record values from NH distribution and associated inference

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Abstract

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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Acknowledgments

The authors thank the referees for their constructive and useful comments and suggestions regarding the first version of this manuscript, which led to this improved version.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1467, Babolsar, Iran

    S. M. T. K. MirMostafaee & A. Asgharzadeh

  2. Department of Statistics, Faculty of Mathematics and Statistics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

    A. Fallah

Authors
  1. S. M. T. K. MirMostafaee
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  2. A. Asgharzadeh
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  3. A. Fallah
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Correspondence to S. M. T. K. MirMostafaee.

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MirMostafaee, S.M.T., Asgharzadeh, A. & Fallah, A. Record values from NH distribution and associated inference. METRON 74, 37–59 (2016). https://doi.org/10.1007/s40300-015-0069-0

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  • DOI: https://doi.org/10.1007/s40300-015-0069-0

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