Abstract
References
- Castaño, M.A., and López, B.F., Distribution of a Sum of Weighted Central Chi- Squared Variables. Communications in Statistics-Theory and Methods, vol. 34; (2005), pp. 515-524.
- Charnes A. and Cooper W. W., Chance-Constrained Programming. Management Sci. 5: (1959), pp. 73-79.
- Feller, W., An Introduction to Probability Theory and Its Applications, Volume II, 1966, John Wiley and Sons, Inc. New York, London.
- Johnson, N.L., Kotz, S., and Balakrishnan, N., Continuous Univariate Distributions I, Second Ed., 1994, New York, John Wiley and Sons.
- Kendall, M.G., The Advanced Theory of Statistics, Volume I, 1945, Charles Gri¢ n Company Limited.
- Lehmann, E.L., Elements of Large Sample Theory, 1999, Springer Verlag, New York Inc.
- Patnaik, P.B., The Non Central Chi-Square and F-Distribution and Their Applications. Biometrika, vol.36; No:1/2, (1949), pp.202-232.
- Sengupta, J.K. A., Generalization of Some Distribution Aspects of Chance Constrained Linear Programming. International Economic Review, vol. 11, (1970), pp. 287-304.
- Wallace, D. L., Asymptotic Approximations to Distributions. The Annals of Mathematical Statistics, Vol. 29, No. 3, (1958), pp. 635-654. Current address : Ankara University, Faculty of Sciences, Department of Statistics, 06100
- Tando¼gan-Ankara, Turkey E-mail address : yilmazm@science.ankara.edu.tr
Abstract
We introduce two methods for approximation to distribution ofweighted sum of chi-square random variables. These methods can be more useful than the known methods in literature to transform chi-square type chanceconstrained programming (CCP) problem into deterministic problem. Therefore, these are compared with Sengupta (1970)’s method. Some examples areillustrated for the purpose of comparing the solutions of these methods
Keywords
weighted sum of chi-square random variables expansion for distributions chance constrained stochastic model
References
- Castaño, M.A., and López, B.F., Distribution of a Sum of Weighted Central Chi- Squared Variables. Communications in Statistics-Theory and Methods, vol. 34; (2005), pp. 515-524.
- Charnes A. and Cooper W. W., Chance-Constrained Programming. Management Sci. 5: (1959), pp. 73-79.
- Feller, W., An Introduction to Probability Theory and Its Applications, Volume II, 1966, John Wiley and Sons, Inc. New York, London.
- Johnson, N.L., Kotz, S., and Balakrishnan, N., Continuous Univariate Distributions I, Second Ed., 1994, New York, John Wiley and Sons.
- Kendall, M.G., The Advanced Theory of Statistics, Volume I, 1945, Charles Gri¢ n Company Limited.
- Lehmann, E.L., Elements of Large Sample Theory, 1999, Springer Verlag, New York Inc.
- Patnaik, P.B., The Non Central Chi-Square and F-Distribution and Their Applications. Biometrika, vol.36; No:1/2, (1949), pp.202-232.
- Sengupta, J.K. A., Generalization of Some Distribution Aspects of Chance Constrained Linear Programming. International Economic Review, vol. 11, (1970), pp. 287-304.
- Wallace, D. L., Asymptotic Approximations to Distributions. The Annals of Mathematical Statistics, Vol. 29, No. 3, (1958), pp. 635-654. Current address : Ankara University, Faculty of Sciences, Department of Statistics, 06100
- Tando¼gan-Ankara, Turkey E-mail address : yilmazm@science.ankara.edu.tr
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | August 1, 2007 |
| Published in Issue | Year 2007 Volume: 56 Issue: 2 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
