In this paper, the ratio of product of two α-k-μ random variables and α-k-μ random variable is analyzed. The closed form expression for average level crossing rate (LCR) of the ratio of product of two α-k-μ random variables and α-k-μ random variable is determined. The expression for level crossing rate of the ratio of product of two α-k-μ random variables and α-k-μ random variable can be used f...

Some different extensions to random sets of the most common parameters of a random variable share a common rationale: a random set represents the imprecise observation of a random variable, hence the generalized parameter contains the available information about the respective parameter of the imprecisely observed variable. Following the same principles, in this paper it is proposed a new defin...

In general case, Chambers et al. (1976) introduced the following algorithm for simulating any stable random variables $ X/sim(alpha, beta, gamma, delta) $ with four parameters. They use a nonlinear transformation of two independent uniform random variables for simulating an stable random variable... (to continue, click here)

Chance theory is put forward as a tool to deal with a complex system including randomness and uncertainty. As a fundamental concept in chance theory, uncertain random variable is an extension of random variable and uncertain variable. This paper obtains a new law of large numbers for independent uncertain random variables but not necessarily identically distributed.

We will show that • the entropy for a random variable gives a lower bound on the number of bits needed per character for a binary coding • Huffman codes are optimal in the average number of bits used per character among binary codes • the average bits per character used by Huffman codes is close to the entropy of the underlying random variable • one can get arbitrarily close to the entropy of a...

Let X be a random variable. We shall call an independent random variable Y to be a symmetrizer forX , ifX+Y is symmetric around zero. If Y is independent copy of −X , it is obviously a symmetrizer. A random variable is said to be symmetry resistant if the variance of any symmetrizer Y , is never smaller than the variance of X itself. For example, let X be a Bernoulli(p) random variable. If p = ...