Journal of the Korean Statistical Society

  • 제35권2호
  • /
  • Pages.167-177
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  • 2006
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  • 1226-3192(pISSN)
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  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

STATISTICAL EVIDENCE METHODOLOGY FOR MODEL ACCEPTANCE BASED ON RECORD VALUES

  • Doostparast M. (Department of Statistics, Ferdowsi University of Mashhad) ;
  • Emadi M. (Department of Statistics, Ferdowsi University of Mashhad)
  • 발행 : 2006.06.01
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초록

An important role of statistical analysis in science is interpreting observed data as evidence, that is 'what do the data say?'. Although standard statistical methods (hypothesis testing, estimation, confidence intervals) are routinely used for this purpose, the theory behind those methods contains no defined concept of evidence and no answer to the basic question 'when is it correct to say that a given body of data represent evidence supporting one statistical hypothesis against another?' (Royall, 1997). In this article, we use likelihood ratios to measure evidence provided by record values in favor of a hypothesis and against an alternative. This hypothesis is concerned on mean of an exponential model and prediction of future record values.

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참고문헌

  1. AHMADI, J. (2000). Record values, theory and applications, Ph.D. Dissertation, Ferdowsi University of Mashhad, Mashhad, Iran
  2. AHMADI, J. AND DOOSTPARAST, M. (2006). 'Bayesian estimation and prediction for some life distributions based on record values', Statistical Papers, to appear
  3. AHMADI, J., DOOSTPARAST, M. AND PARSIAN, A. (2005). 'Estimation and prediction in a two-parameter exponential distribution based on k-record values under LINEX loss function', Communications in Statistics-Theory and Methods, 34, 795-805 https://doi.org/10.1081/STA-200054393
  4. AHSANULLAH, M. (1995). Record Statistics, Nova Science Publishers, New York
  5. AHSANULLAH, M. (1980). 'Linear prediction of record values for the two-parameter exponential distribution', Annals of the Institute of Statistical Mathematics, 32, 363-368 https://doi.org/10.1007/BF02480340
  6. ARNOLD, B. C., BALAKRISHNAN, N. AND NAGARAJA, H. N. (1998). Records, John Wiley & Sons, New York
  7. BERRED, A. M. (1998). 'Prediction of record values', Communications in Statistics-Theory and Methods, 27, 2221-2240 https://doi.org/10.1080/03610929808832224
  8. CHANDLER, K. N. (1952). 'The distribution and frequency of record value,', Journal of the Royal Statistical Society, Ser. B, 14, 220-228
  9. EMADI, M. AND ARGHAMI, N. R. (2003). 'Some measures of support for statistical hypotheses', Journal of Statistical Theory and Applications, 2, 165-176
  10. FEUERVERGER, A. AND HALL, P. (1998). 'On statistical inference based on record values', Extremes, 1, 169-190 https://doi.org/10.1023/A:1009958722622
  11. GLICK, N. (1978). 'Breaking record and breaking boards', The American Mathematical Monthly, 85, 2-26 https://doi.org/10.2307/2978044
  12. GULATI, S. AND PADGETT, W. J. (2003). Parametric and Nonparametric Inference from Record-breaking Data, Springer-Verlag, New York
  13. NEVZOROV, V. B. (2001). Records: Mathematical Theory. Translated from the Russian Manuscript by D. M. Chibisov, American Mathematical Society, Providence, RI
  14. ROYALL, R. M. (1997). Statistical Evidence. A Likelihood Paradigm, Chapman and Hall, London
  15. ROYALL, R. M (2000). 'On the probability of observing misleading statistical evidence', Journal of the American Statistical Association, 95, 760-780 https://doi.org/10.2307/2669456
  16. SAMANIEGO, F. J. AND WHITAKER, L. R. (1986). 'On estimating population characteristics from record-breaking observations. I. Parametric results.', Naval Research Logistics Quarterly, 33, 531-543 https://doi.org/10.1002/nav.3800330317