Kybernetika 50 no. 5, 744-757, 2014

Hypotheses testing with the two-parameter Pareto distribution on the basis of records in fuzzy environment

Ali Reza Saeidi, Mohammad Ghasem Akbari and Mahdi DoostparastDOI: 10.14736/kyb-2014-5-0744


In problems of testing statistical hypotheses, we may be confronted with fuzzy concepts. There are also situations in which the available data are record statistics such as weather and sports. In this paper, we consider the problem of testing fuzzy hypotheses on the basis of records. Pareto distribution is investigated in more details since it is used in applications including economic and life testing analysis. For illustrative proposes, a real data set on annual wage is analyzed using the results obtained.


decision analysis, fuzzy hypotheses, pareto distribution, record data, testing hypotheses


62F03, 62A86


  1. M. G. Akbari and M. Arefi: Statistical nonparametric test based on the intuitionistic fuzzy data. J. Intell. Fuzzy Systems 25 (2013), 525-534.   CrossRef
  2. M. G. Akbari and A. Rezaei: An uniformly minimum variance unbiased point estimator using fuzzy observations. Austrian J. Statist. 36 (2007), 307-317.   CrossRef
  3. M. G. Akbari and A. Rezaei: Bootstrap statistical inference for the variance based on fuzzy data. Austrian J. Statist. 38 (2009), 121-130.   CrossRef
  4. M. G. Akbari, A. Rezaei and Y. Waghei: Statistical inference about the variance of fuzzy random variables. Sankhya 71-B (2009), 1-15.   CrossRef
  5. M. G. Akbari and A. Rezaei: Bootstrap testing fuzzy hypotheses and observations on fuzzy statistic. Expert Systems Appl. 37 (2010), 8, 5782-5787.   CrossRef
  6. B. C. Arnold: Pareto Distributions. International Co-operative Publishing House, Fairland 1983.   CrossRef
  7. B. C. Arnold, N. Balakrishnan and H. N. Nagaraja: Records. John Wiley and Sons, New York 1998.   CrossRef
  8. B. F. Arnold: An approach to fuzzy hypothesis testing. Metrika 44 (1996), 119-126.   CrossRef
  9. B. F. Arnold: Testing fuzzy hypotheses with crisp data. Fuzzy Sets and Systems 94 (1998), 323-333.   CrossRef
  10. J. J. Buckley: Fuzzy Probabilities: New Approach and Applications. Springer-Verlag, Berlin, Heidelberg 2005.   CrossRef
  11. J. J. Buckley: Fuzzy Probability and Statistics. Springer-Verlag, Berlin, Heidelberg 2006.   CrossRef
  12. M. Delgado, J. L. Verdegay and M. A. Vila: Testing fuzzy hypotheses, a Bayesian approach. In: Approximate Reasoning in Expert Systems (M. M. Gupta, ed.) 1985, pp. 307-316.   CrossRef
  13. M. Doostparast, M. G. Akbari and N. Balakrishnan: Bayesian analysis for the two-parameter Pareto distribution based on record values and times. J. Stat. Comput. Simul. 81 (2011), 11, 1393-1403.   CrossRef
  14. M. Doostparast and N. Balakrishnan: Pareto record-based analysis. Statistics 47 (2013), 5, 1075-1089.   CrossRef
  15. D. Dyer: Structural probability bounds for the strong Pareto laws. Canad. J. Statist. 9 (1981), 71-77.   CrossRef
  16. P. Filzmoser and R. Viertl: Testing hypotheses with fuzzy data: the fuzzy $p-$value. Metrika 59 (2004), 21-29.   CrossRef
  17. G. Gonzalez-Rodriguez, M. Montenegro, A. Colubi and M. A. Gil: Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data. Fuzzy Sets and Systems 157 (2006), 2608-2613.   CrossRef
  18. S. Gulati and W. J. Padgett: Smooth nonparametric estimation of the distribution and density functions from record-breaking data. Commun. Commun. Statist. - Theory and Methods {\mi 23} (1994), 1259-1274.   CrossRef
  19. M. Holena: Fuzzy hypotheses for GUHA implications. Fuzzy Sets and Systems 98 (1998), 101-125.   CrossRef
  20. M. Holena: Fuzzy hypotheses testing in the framework of fuzzy logic. Fuzzy Sets and Systems 145 (2004), 229-252.   CrossRef
  21. R. Körner: An asymptotic $\alpha-$cut for the expectation of random fuzzy variables. J. Statist. Plann. Inferences 83 (2000), 331-346.   CrossRef
  22. M. Montenegro, A. Colubi, M. R. Casals and M. A. Gil: Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59 (2004), 31-49.   CrossRef
  23. A. Parchami, S. M. Taheri and M. Mashinchi: Fuzzy p-value in testing fuzzy hypotheses with crisp data. Statist. Papers 51 (2010), 1, 209-226.   CrossRef
  24. F. J. Samaniego and L. R. Whitaker: On estimating population characteristics from record-breaking observations II: NonParametric results. Naval Res. Logist. 35 (1988), 221-236.   CrossRef
  25. S. M. Taheri and M. Arefi: Testing fuzzy hypotheses based on fuzzy statistics. Soft Computing 13 (2009), 617-625.   CrossRef
  26. S. M. Taheri and J. Behboodian: Neyman-Pearson lemma for fuzzy hypotheses testing. Metrika 49 (1999), 3-17.   CrossRef
  27. H. Torabi, J. Behboodian and S. M. Taheri: Neyman-Pearson Lemma for fuzzy hypotheses testing with vague data. Metrika 64 (2006), 289-304.   CrossRef
  28. R. Viertl: Univariate statistical analysis with fuzzy data. Comput. Statist. Data Anal. {\mi 51} (2006), 133-147.   CrossRef
  29. J. S. Yao and K. Wu: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems 11 (2000), 275-288.   CrossRef