Randomly Weighted Averages on Order Statistics

Homei Hajir, Hasanzadeh Leila, Mina Ghasemi

Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

DOI: 10.4236/am.2013.49181                

Abstract

We study a well-known problem concerning a random variable uniformly distributed between two independent random variables. Two different extensions, randomly weighted average on independent random variables and randomly weighted average on order statistics, have been introduced for this problem. For the second method, two-sided power random variables have been defined. By using classic method and power technical method, we study some properties for these random variables.

Keywords

Two-Sided Power; Moment; Weighted Averages; Power Distribution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. Van Asch, “A Random Variable Uniformly Distributed between Two Independent Random Variables,” Sankhaya, Vol. 49, No. 2, 1987, pp. 207-211. doi:10.1080/00031305.1990.10475730
[2]	A. R. Soltani and H. Homei, “Weighted Averages with Random Proportions That Are Jointly Uniformly Distributed over the Unit Simplex,” Statistics & Probability Letters, Vol. 79, No. 9, 2009, pp. 1215-1218. doi:10.1016/j.spl.2009.01.009
[3]	N. L. Johnson and S. Kotz, “Randomly Weighted Averages,” The American Statistician, Vol. 44, No. 3, 1990, pp. 245-249. doi:10.2307/2685351
[4]	A. I. Zayed, “Handbook of Function and Generalized Function Transformations,” CRC Press, London, 1996.
[5]	A. R. Soltani and H. Homei, “A Generalization for TwoSided Power Distributions and Adjusted Method of Moments,” Statistics, Vol. 43, No. 6, 2009, pp. 611-620. doi:10.1080/02331880802689506