Representing and approximating symmetric and asymmetric probability coverage intervals by possibility distributions

IEEE Transactions on Instrumentation and Measurement

Volumn 58, Issue 1, 2009, Pages 41-45

  Mauris, Gilles ^a  

^a Université de Savoie   (France)

Author keywords

Asymmetric distributions; Coverage intervals; Measurement uncertainty; Possibility theory; Statistical tests

Indexed keywords

DECODING; IMAGE SEGMENTATION; PROBABILITY; RANDOM PROCESSES; STATISTICAL TESTS; UNCERTAINTY ANALYSIS;

APPLICATION LEVELS; ASYMMETRIC DISTRIBUTIONS; CLOSED FORMS; COVERAGE INTERVALS; KEY COMPARISONS; MEASURED VALUES; MEASUREMENT RESULTS; MEASUREMENT UNCERTAINTY; POSSIBILITY DISTRIBUTIONS; POSSIBILITY THEORY; PROBABILISTIC REPRESENTATIONS; PROBABILITY COVERAGES; PROBABILITY DENSITIES; UNIMODAL;

PROBABILITY DISTRIBUTIONS;

EID: 57949110341     PISSN: 00189456     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIM.2008.2004980     Document Type: Conference Paper

References (20)

1. L. Mari and G. Zingales, "Uncertainty in measurement science," in Proc. Int. Workshop Adv. Meas. Sci., Kyoto, Japan, 1999, pp. 177-189.
2. L. Mari, "Notes on the uncertainty of measurement," in Proc. 15th IMEKO World Congr., Osaka, Japan, 1999, vol. II, pp. 89-92.
3. L. Reznik and K. P. Dabke, "Evaluation of uncertainty in measurement: A proposal for application of intelligent methods," in Proc. 15th IMEKO World Congr., Osaka, Japan, 1999, vol. 11, pp. 93-100.
4. Guide for the Expression of Uncertainty in Measurement, 1993. ISO 1993, 99 pp.
5. M. Kendall and A. Stuart, The Advanced Theory of Statistics. London, U.K.: Griffin, 1977.
6. R. Moore, Interval Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1966.
7. D. Dubois and H. Prade, "On several representations of an uncertain body of evidence," in Fuzzy Information and Decision Processes, M. M. Gupta and E. Sanchez, Eds. Amsterdam, The Netherlands: North-Holland, 1982, pp. 167-181.
8. S. Moral, "Construction of a probability distribution from a fuzzy information," in Fuzzy Sets Theory and Applications, A. Jones, A. Kauffmann, and H. J. Zimmermann, Eds. Amsterdam, The Netherlands: Reidel, 1986, pp. 51-60.
9. D. Dubois, H. Prade, and S. Sandri, "On possibility/probability transformations," in Fuzzy Logic, R. Lowen and M. Roubens, Eds. Norwell, MA: Kluwer, 1993, pp. 103-112.
10. G. Mauris, V. Lasserre, and L. Foulloy, "Fuzzy modeling of measurement data acquired from physical sensors," IEEE Trans. Instrum. Meas., vol. 49, no. 6, pp. 1201-1205, Dec. 2000.
11. M. Urbanski and J. Wasowki, "Fuzzy approach to the theory of measurement inexactness," Meas., vol. 34, no. 1, pp. 67-74, Jul. 2003.
12. A. Ferrero and S. Salicone, "The random-fuzzy variables: A new approach to the expression of uncertainty in measurement," IEEE Trans. Instrum. Meas., vol. 53, no. 5, pp. 1370-1377, Oct. 2004.
13. G. Mauris, V. Lasserre, and L. Foulloy, "A fuzzy approach for the expression of uncertainty in measurement," Meas., vol. 29, no. 3, pp. 165-177, Mar. 2001.
14. L. A. Zadeh, "Fuzzy sets as a basis for a theory of possibility," Fuzzy Sets Syst., vol. 1, no. 1, pp. 3-28, 1978.
15. G. Mauris, "Expression of measurement uncertainty in a very limited knowledge context: A possibility theory-based approach," IEEE Trans. Instrum. Meas., vol. 56, no. 3, pp. 731-735, Jun. 2007.
16. D. Dubois, L. Foulloy, G. Mauris, and H. Prade, "Probability-possibility transformations, triangular fuzzy sets and probabilistic inequalities," Reliab. Comput., vol. 10, no. 4, pp. 273-297, Aug. 2004.
17. C. Perruchet, "Some differences between the applied statistical approach for measurement uncertainty theory and the traditional approach in metrology and testing," in Advanced Mathematical and Computational Tools in Metrology VI, P. Ciarlini, M. Cox, F. Pavese, and G. Rossi, Eds. Singapore: World Scientific, 2004, pp. 98-105.
18. G. Mauris, "Approximating coverage intervals of well-known continuous probability distributions by possibility distributions," in Proc. IEEE Workshop AMUEM, Trento, Italy, 2007, pp. 5-9.
19. A. G. Steele and R. J. Douglas, "Extending chi-squared statistics for key comparisons in metrology," J. Comput. Appl. Math., vol. 192, no. 1, pp. 51-58, Jul. 2006.
20. D. Sengupta and A. K. Nanda, "Log-concave and concave distributions in reliability," Nav. Res. Logist., vol. 46, no. 4, pp. 419-433, Apr. 1999.