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.
Cite this paper
H. Hajir, H. Leila and M. Ghasemi, "Randomly Weighted Averages on Order Statistics," Applied Mathematics
, Vol. 4 No. 9, 2013, pp. 1340-1346. doi: 10.4236/am.2013.49181
 W. Van Asch, “A Random Variable Uniformly Distributed between Two Independent Random Variables,” Sankhaya, Vol. 49, No. 2, 1987, pp. 207-211.
 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.
 N. L. Johnson and S. Kotz, “Randomly Weighted Averages,” The American Statistician, Vol. 44, No. 3, 1990, pp. 245-249. doi:10.2307/2685351
 A. I. Zayed, “Handbook of Function and Generalized Function Transformations,” CRC Press, London, 1996.
 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.