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NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY

Year 2013, Volume: 6 Issue: 2, 66 - 72, 01.07.2013

Turkan Erbay Dalkilic , Tulay Kesemen , Fatih Tank

Abstract

References

  • Buckley, J.J., 2006, Fuzzy Probability and Statistics, Springer-Verlag, Berlin Heidelberg.
  • Buckley, J.J., 1987, The Fuzzy Mathematic of Finance, Fuzzy Sets and Syst., 21, 257-273.
  • Buckley, J.J. and Eslami, E., 2004, Uncertain Probabilities II: The Continuous Case, Soft Computing, 8, 193-199.
  • Carretero, R.C., Viejo, A.S., 2000, A Bonus-Malus System in The Fuzzy Set Theory [insurance pricing decisions]. IEEE Int.-Conf. Fuzzy Syst. 2, 1036-1036.
  • Cramer, H., 1963, Mathematical Methods of Statistics, Princeton University Press.
  • Dubois, D. and Prade, H., 1980, Fuzzy Sets and Systems: Theory and Application, Academic, New York.
  • Ebanks, B., Kanvowski, W., Ostaszewski, K.M., 1992, Application of Measures of Fuzziness to Risk Classification in Insurance, In: Computing and Information. IEEE Computer Society Press, Los Alamitos, CA, 290-291.
  • Feng, Y., Hu, L., Shu, H., 2001, The Variance and Covariance of Fuzzy Random Variables and Their Applications, 120, 487-497.
  • Garcia, J.N., Kutalik, Z., Cho, K.H. and Wolkenhauer, O., 2003, Level Sets and Minimum Volume Sets of Probability Density Functions, International Journal of Approximate-Reasoning 34, 25-47.
  • Johnson, N.L., Kotz, S. and Balakrishnan, N., 1995. Continuous Univariate Distributions (2nd Edition, Vol. 1 ed.), Wiley, New York.
  • Kleiber, C., Kotz, S., 2003, Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley & Sons, Hoboken NJ.
  • K¨orner, R., 1997, On the Variance of Fuzzy Random Variables, Fuzzy Set and Systems, 92, 83-93.
  • Lemaire, J. 1990, Fuzzy Insurance, ASTIN Bull. 20(1), 33-55.
  • Meyer, P.L.,1970, Introductory Probability and Statistical Applications, Second Edition, AddisonWesley Publishing Company, USA.
  • Muzzioli, S., Reyna, H., 2008, American Option Pricing With Imprecise Risc-Neutral Probabilities, International Journal of Approximate-Reasoning 49, 140-147.
  • Shapiro, A.F., 2004, Fuzzy Logic in Insurance, Insurance: Mathematics and Economics, 35, 399-424.
  • Wang, L.X., 1997, A Course in Fuzzy Systems and Control, Prentice Hall PRT, USA.
  • Young, V.R., 1996, Insurance Rate Changing: a Fuzzy Logic Approach. J. Risk Insurance, 63, 461-483.
  • Zadeh, L.A.,1965, Fuzzy Set. Information Control, 8, 338-353.
  • Zimmermann, H., 1996, Fuzzy Set Theory and Its Applications, Third ed. Kluwer Academic Publishers, Boston, USA.
  • Zisheng O., Chi, X., 2006, Generalized Pareto Distribution Fit to Medical Insurance Claim Data, Appl. Math. J. Chinese Univ. Ser. B. 21(1), 21-29.

NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY

Year 2013, Volume: 6 Issue: 2, 66 - 72, 01.07.2013

Turkan Erbay Dalkilic , Tulay Kesemen , Fatih Tank

Abstract

In this study, we consider the Pareto distribution where the value of k parameter is uncertain.
Some statistical quantities such as expected value, variance, skewness and kurtosis of the pareto distribution
are derived by using fuzzy numbers. In addition to the these numerical characteristics, a numerical study
is provided. Furthermore, large claims data from Society of Actuaries (SOA) Group Medical insurance is examined and k parameter of Pareto distribution is obtained by using the maximum likelihood estimation
method and the numerical characteristics of this distribution are calculated under uncertainty

Keywords

Pareto distribution uncertain probability medical insurance

References

  • Buckley, J.J., 2006, Fuzzy Probability and Statistics, Springer-Verlag, Berlin Heidelberg.
  • Buckley, J.J., 1987, The Fuzzy Mathematic of Finance, Fuzzy Sets and Syst., 21, 257-273.
  • Buckley, J.J. and Eslami, E., 2004, Uncertain Probabilities II: The Continuous Case, Soft Computing, 8, 193-199.
  • Carretero, R.C., Viejo, A.S., 2000, A Bonus-Malus System in The Fuzzy Set Theory [insurance pricing decisions]. IEEE Int.-Conf. Fuzzy Syst. 2, 1036-1036.
  • Cramer, H., 1963, Mathematical Methods of Statistics, Princeton University Press.
  • Dubois, D. and Prade, H., 1980, Fuzzy Sets and Systems: Theory and Application, Academic, New York.
  • Ebanks, B., Kanvowski, W., Ostaszewski, K.M., 1992, Application of Measures of Fuzziness to Risk Classification in Insurance, In: Computing and Information. IEEE Computer Society Press, Los Alamitos, CA, 290-291.
  • Feng, Y., Hu, L., Shu, H., 2001, The Variance and Covariance of Fuzzy Random Variables and Their Applications, 120, 487-497.
  • Garcia, J.N., Kutalik, Z., Cho, K.H. and Wolkenhauer, O., 2003, Level Sets and Minimum Volume Sets of Probability Density Functions, International Journal of Approximate-Reasoning 34, 25-47.
  • Johnson, N.L., Kotz, S. and Balakrishnan, N., 1995. Continuous Univariate Distributions (2nd Edition, Vol. 1 ed.), Wiley, New York.
  • Kleiber, C., Kotz, S., 2003, Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley & Sons, Hoboken NJ.
  • K¨orner, R., 1997, On the Variance of Fuzzy Random Variables, Fuzzy Set and Systems, 92, 83-93.
  • Lemaire, J. 1990, Fuzzy Insurance, ASTIN Bull. 20(1), 33-55.
  • Meyer, P.L.,1970, Introductory Probability and Statistical Applications, Second Edition, AddisonWesley Publishing Company, USA.
  • Muzzioli, S., Reyna, H., 2008, American Option Pricing With Imprecise Risc-Neutral Probabilities, International Journal of Approximate-Reasoning 49, 140-147.
  • Shapiro, A.F., 2004, Fuzzy Logic in Insurance, Insurance: Mathematics and Economics, 35, 399-424.
  • Wang, L.X., 1997, A Course in Fuzzy Systems and Control, Prentice Hall PRT, USA.
  • Young, V.R., 1996, Insurance Rate Changing: a Fuzzy Logic Approach. J. Risk Insurance, 63, 461-483.
  • Zadeh, L.A.,1965, Fuzzy Set. Information Control, 8, 338-353.
  • Zimmermann, H., 1996, Fuzzy Set Theory and Its Applications, Third ed. Kluwer Academic Publishers, Boston, USA.
  • Zisheng O., Chi, X., 2006, Generalized Pareto Distribution Fit to Medical Insurance Claim Data, Appl. Math. J. Chinese Univ. Ser. B. 21(1), 21-29.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Turkan Erbay Dalkilic

Tulay Kesemen

Fatih Tank 0000-0003-3758-396X

Publication Date July 1, 2013
Acceptance Date March 3, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

APA Erbay Dalkilic, T., Kesemen, T., & Tank, F. (2013). NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY. Istatistik Journal of The Turkish Statistical Association, 6(2), 66-72.
AMA Erbay Dalkilic T, Kesemen T, Tank F. NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY. IJTSA. July 2013;6(2):66-72.
Chicago Erbay Dalkilic, Turkan, Tulay Kesemen, and Fatih Tank. “NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY”. Istatistik Journal of The Turkish Statistical Association 6, no. 2 (July 2013): 66-72.
EndNote Erbay Dalkilic T, Kesemen T, Tank F (July 1, 2013) NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY. Istatistik Journal of The Turkish Statistical Association 6 2 66–72.
IEEE T. Erbay Dalkilic, T. Kesemen, and F. Tank, “NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY”, IJTSA, vol. 6, no. 2, pp. 66–72, 2013.
ISNAD Erbay Dalkilic, Turkan et al. “NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY”. Istatistik Journal of The Turkish Statistical Association 6/2 (July 2013), 66-72.
JAMA Erbay Dalkilic T, Kesemen T, Tank F. NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY. IJTSA. 2013;6:66–72.
MLA Erbay Dalkilic, Turkan et al. “NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY”. Istatistik Journal of The Turkish Statistical Association, vol. 6, no. 2, 2013, pp. 66-72.
Vancouver Erbay Dalkilic T, Kesemen T, Tank F. NUMERICAL CHARACTERISTICS OF PARETO DISTRIBUTION UNDER UNCERTAINTY. IJTSA. 2013;6(2):66-72.
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