PARAMETER ESTIMATION FOR PARETO DISTRIBUTION AND TYP E-I I FUZZY LOGIC

Abstract

While parameter estimation by the classical methods there are a
number of assumptions need to be satisfied, in the linear regression analysis. One of them is errors are normally distributed. In this work, the case that independent variable has Pareto distribution to be discussed and an algorithm using adaptive networks suggested to parameter estimation where the k which is one of the parameters of the fuzzy membership functions is fuzzy. Also the parameter of fuzzy membership function is fuzzy the estimation process is based on type-II fuzzy logic.

Keywords

• Pareto distribution,type-II fuzzy logic,membership function

References

1. Aisb ett, J., Rickart, J. T., Morgenthaler, D., Multivariate mo deling and typ e-2 fuzzysets, Fuzzy Sets and Systems 163 (2011) 78-95.
2. Castillo, O., Melin, P. Typ e-2 fuzzylogic: theory and applications, Sipringer, (2008).
3. Cheng, C.B., Lee , E.S., Switching regression analysis by fuzzy adaptive network, Europ en
4. Journal of Op erational Research 128 (2001) 647-668.
5. Civanlar , M.R., Trussell, H.J., Constructing memb ership functions using statistical data
6. fuzzy sets and systems, 18 (1986) 1-13
7. Cramer, H. ,Mathematical metho ds of statistics, Princeton University Press, (1963).
8. Hisao, I., Manabu, N., Fuzzy regression using asymmetric fuzzy co efficients and fuzzied neural

9. networks, Fuzz y Sets and Systems 119 (2001) 273-290.
10. Karnik N.K., Mendel, J.M.,Typ e-2 Fuzz y logic systems, IEEE Transaction on FuzzySystems
11. (1999) 643-658.
12. Karnik N.K., Mendel, J.M., Op erations on typ e-2 fuzzy sets, Fuzzy Sets and Systems 122
13. (2002) 327-348.
14. Mendel, J.M., John, R.I.B. , Typ e-2 fuzzy sets made simple, IEEE Transaction on FuzzySystems 10 (2002) 117-127.
15. Mendel, J. M., Typ e-2 fuzzy sets and systems: A n overview, IEEE Computational Intel ligence
16. Magazine Fabuary (2007) 21-29.
17. Mendel, J. M., Advances in typ e-2 fuzzy sets and systems, Information Sciences 177 (2007)
18. -110.
19. Meyer, P.L., Intro ductory probabili ty and statistical applications, Second Edition, AddisonWesl ey Publishing Company, USA, (1970).
20. Turksen, I.B., Typ e I and Typ e I I fuzzy systems mo delling, Fuzzy Sets and Systems 106
21. (1999) 11-34.
22. Zisheng O., Chi, X., Generalized pareto distribution fit to medical insurance claim data,
23. Appl. Math. J. Chinese Univ. Ser. B. 21 (2006) 21-29.