Fuzzy Estimation of Parameters in Statistical Models
Using a set of confidence intervals, we develop a
common approach, to construct a fuzzy set as an estimator for
unknown parameters in statistical models. We investigate a method
to derive the explicit and unique membership function of such fuzzy
estimators. The proposed method has been used to derive the fuzzy
estimators of the parameters of a Normal distribution and some
functions of parameters of two Normal distributions, as well as the
parameters of the Exponential and Poisson distributions.
[1] Bakhshi M, Mashinchi M, Borzooei R (2006) Representation theorem
for some fuzzy algebraic hyperstructures, International Review of Fuzzy
Mathematics, Volume 1. No. 1: 73-87.
[2] Buckley JJ (2005) Fuzzy statistics: hypothesis testing. Soft Comput 9:
512-518.
[3] Casella G, Berger R L (2001) Statistical Inferences, Sec. Ed., Duxbury
Press.
[4] Hogg RV, Tanis EA (2001) Probability and Statistical Inference, 6th Ed.,
Prentice-Hall, Upper Saddle River.
[5] Johnson RA, Bhattacharyya GK (2000) Statistics: Principles and Methods,
Fourth Ed., John Wiley, New York.
[6] Klir GJ, Yuan B (1995) Fuzzy Sets and Fuzzy Logic Theory and
Applications, Prentice-Hall, Englewood Cliffs, NJ.
[7] Maple 10 (2006) Waterloo Maple Inc., Waterloo, Canada.
[8] Nguyen HT, Walker EA (2006) A First Course in Fuzzy Logic, Third
Edition, Chapman & Hall/ CRC, Taylor and Francis Group, Boca Rotan,
New York.
[9] Rohatgi VK, Ehsan Saleh AK (2001) An Introduction to Probability
Theory and Mathematical Statistics, Sec. Ed., John Wiley, New York.
[1] Bakhshi M, Mashinchi M, Borzooei R (2006) Representation theorem
for some fuzzy algebraic hyperstructures, International Review of Fuzzy
Mathematics, Volume 1. No. 1: 73-87.
[2] Buckley JJ (2005) Fuzzy statistics: hypothesis testing. Soft Comput 9:
512-518.
[3] Casella G, Berger R L (2001) Statistical Inferences, Sec. Ed., Duxbury
Press.
[4] Hogg RV, Tanis EA (2001) Probability and Statistical Inference, 6th Ed.,
Prentice-Hall, Upper Saddle River.
[5] Johnson RA, Bhattacharyya GK (2000) Statistics: Principles and Methods,
Fourth Ed., John Wiley, New York.
[6] Klir GJ, Yuan B (1995) Fuzzy Sets and Fuzzy Logic Theory and
Applications, Prentice-Hall, Englewood Cliffs, NJ.
[7] Maple 10 (2006) Waterloo Maple Inc., Waterloo, Canada.
[8] Nguyen HT, Walker EA (2006) A First Course in Fuzzy Logic, Third
Edition, Chapman & Hall/ CRC, Taylor and Francis Group, Boca Rotan,
New York.
[9] Rohatgi VK, Ehsan Saleh AK (2001) An Introduction to Probability
Theory and Mathematical Statistics, Sec. Ed., John Wiley, New York.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63392", author = "A. Falsafain and S. M. Taheri and M. Mashinchi", title = "Fuzzy Estimation of Parameters in Statistical Models", abstract = "Using a set of confidence intervals, we develop a
common approach, to construct a fuzzy set as an estimator for
unknown parameters in statistical models. We investigate a method
to derive the explicit and unique membership function of such fuzzy
estimators. The proposed method has been used to derive the fuzzy
estimators of the parameters of a Normal distribution and some
functions of parameters of two Normal distributions, as well as the
parameters of the Exponential and Poisson distributions.", keywords = "Confidence interval. Fuzzy number. Fuzzy estimation.", volume = "2", number = "2", pages = "159-7", }