Cumulant Generating Function and Tail Probability Approximations for Kendall's Score with Tied Rankings

Optimality Theoretic Rankings with Tied Constraints :

Probability Generating Functions for Sattolo’s Algorithm

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...

Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression Allowing Positive Excess Distortion Probability

This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit of the cumulant generating function of codeword lengths allowing positive excess distortion probability. It is shown that the achievability and converse bound...

Priority queueing systems: from probability generating functions to tail probabilities

Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabil...

Nonstationary Loss Queues via Cumulant Moment Approximations