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METRON

, Volume 72, Issue 1, pp 65–76 | Cite as

Generalized exponential records: existence of maximum likelihood estimates and its comparison with transforming based estimates

  • Mohammad Z. RaqabEmail author
  • Khalaf S. Sultan
Article

Abstract

In this paper, and based on records of a sequence of iid random variables from the generalized exponential distribution, we consider the problem of the existence of the maximum likelihood estimates of the shape and scale parameters. Existence and uniqueness of the MLE’s are proved. Different transforming based estimates and confidence intervals of these parameters are then derived. The performances of the so obtained estimates and confidence intervals are compared through an extensive numerical simulation study. Analysis of a real data set has also been presented for illustrative purposes.

Keywords

Record statistics Generalized exponential distribution  Maximum likelihood estimate Pivotal quantity  Confidence interval Uniform distribution Exponential distribution 

Mathematics Subject Classification

62G30 62E15 62F10 

Notes

Acknowledgments

The authors are grateful to the associate editor and referees for their helpful comments and suggestions.

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Copyright information

© Sapienza Università di Roma 2013

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchKuwait UniversitySafatKuwait
  2. 2.Department of Statistics and Operation ResearchKing Saud UniversityRiyadhKingdom of Saudi Arabia

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