Freely independent random variables with non-atomic distributions

Addition of Freely Independent Random Variables

Ordered Random Variables from Discontinuous Distributions

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...

Characterizations of Distributions of Ratio of Certain Independent Random Variables

Various characterizations of the distributions of the ratio of two independent gamma and exponential random variables as well as that of two independent Weibull random variables are presented. These characterizations are based, on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics. Mathematics Subject Classification 2000: 46F10

Recursive random variables with subgaussian distributions

with K, n0 ≥ 1, (X n )n≥0 identically distributed as (Xn)n≥0 for r = 1, . . . , K , a random vector I (n) = (I (n) 1 , . . . , I (n) K ) of integers in {0, . . . , n − 1} and a random bn such that (X n )n≥0, . . . , (X ) n )n≥0, (I (n), bn) are independent. The symbol d = denotes equality in distribution. In applications, the I (n) r are random subgroup sizes, bn is a toll function specifying t...

Pairwise Independent Random Variables

In this lecture we discuss how to derandomize algorithms. We will see a brute force algorithm (enumeration) for derandomization. We will also see that some random algorithms do not need true randomness. Specifically, we will see an example where only pairwise random bits are needed. Next, we will see how we can generate pairwise random values and how this conservation on the amount of randomnes...