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Comparing two sampling schemes based on entropy of record statistics

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Abstract

In a number of situations such as industrial quality control experiments the only observations are record-breaking data. In this paper, two sampling schemes are used to collect record data: single sample and multisample. The aim of this paper is to investigate which one of them is more efficient in the sense of Shannon information. Several general results are established and it is shown that there is a connection between some reliability properties of the parent distribution and the considered comparison criterion. A number of examples illustrating the results are given.

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References

  • Ahmadi J, Fashandi M (2008) Shannon information properties of the endpoints of record coverage. Commun Stat Theory Methods 37: 481–493

    Article  MathSciNet  MATH  Google Scholar 

  • Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York

    Book  MATH  Google Scholar 

  • Baratpour S, Ahmadi J, Arghami NR (2007a) Entropy properties of record statistics. Statist Pap 48: 197–213

    Article  MathSciNet  MATH  Google Scholar 

  • Baratpour S, Ahmadi J, Arghami NR (2007b) Some characterizations based on entropy of order statistics and record values. Commun Stat Theory Methods 36: 47–57

    Article  MathSciNet  MATH  Google Scholar 

  • Cover TM, Thomas JA (1991) Elements of information theory. Wiley-Inter science Publication, New York

    Book  MATH  Google Scholar 

  • Gulati S, Padgett WJ (2003) Parametric and nonparametric inference from record-breaking data. Lecture Notes in Statistics 172. Springer, New York

    Google Scholar 

  • Gut A (2007) Probability: a graduate course. Springer, New York

    MATH  Google Scholar 

  • Habibi A, Yousefzadeh F, Amini M, Arghami NR (2007) Testing exponentially based on record values. JIRSS 6(1): 77–87

    MathSciNet  Google Scholar 

  • Raqab MZ, Awad AM (2000) Characterizations of the Pareto and related distributions. Metrika 52: 63–67

    Article  MathSciNet  MATH  Google Scholar 

  • Samaniego FJ, Whitaker LR (1988) On estimating population characteristics from record-breaking observations. II: nonparametric results. Naval Res Logist Q 35: 221–236

    Article  MathSciNet  MATH  Google Scholar 

  • Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York

    Book  MATH  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27: 379–423

    MathSciNet  MATH  Google Scholar 

  • Verdu S (1998) Fifty years of Shannon theory. IEEE Trans Inf Theory 44: 2057–2078

    Article  MathSciNet  MATH  Google Scholar 

  • Zahedi H, Shakil M (2006) Properties of entropies of record values in reliability and life testing context. Commun Stat Theory Methods 35: 997–1010

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 91775-1159, Mashhad, Iran

    M. Razmkhah, H. Morabbi & J. Ahmadi

Authors
  1. M. Razmkhah
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  2. H. Morabbi
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  3. J. Ahmadi
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Correspondence to M. Razmkhah.

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Razmkhah, M., Morabbi, H. & Ahmadi, J. Comparing two sampling schemes based on entropy of record statistics. Stat Papers 53, 95–106 (2012). https://doi.org/10.1007/s00362-010-0316-7

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  • DOI: https://doi.org/10.1007/s00362-010-0316-7

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