The mean time to extinction of a critical Galton–Watson process with initial population size k is shown to be asymptotically equivalent to two integral transforms: one involving the kth iterate of the probability generating function and one involving the generating function itself. Relating the growth of these transforms to the regular variation of their arguments, immediately connects statemen...

existence of capacity drop phenomenon, as the difference between pre-queue and queue discharge flow rates, has been one of the controversial concepts of traffic engineering. several researches have focused on capacity drop existence and also its estimation issues. this paper aims to estimate capacity drop based not only on a comparison between breakdown and queue discharge flow rates, but also ...

This letter provides a novel, efficient numerical solution to evaluate the moment generating function of a Suzuki probability density function using the sampling theorem. Applications include outage probability calculations for mobile radio networks in Rayleigh fading and shadowing.

This paper presents Genpex, a system for automatic generation of narrative probability exercises. Generation of exercises in Genpex is done in two steps. First, the system creates a specification of a solvable probability problem, based on input from the user (a researcher or test developer) who selects a specific question type and a narrative context for the problem. Then, a text expressing th...

A new discrete class of life distributions is studied. This class is defined based on comparing the residual life time to the whole life in the probability generating function order giving “the discrete new better than used in the probability generating function order ageing class (d−NBUpg)”. Fundamental properties of this class are given including some closure properties and characterizations....

1 Branching processes in random environment In this lecture fundamental properties of branching processes in a random environment are developed. In such a process individuals reproduce independently of each other according to random offspring distributions which vary from one generation to the other. To give a formal definition let P = {π} be the space of probability measures on N 0 Equipped wi...

the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...

The purpose of this paper is to justify the claim that a method for generating primes presented at EUROCRYPT'89 generates primes with virtually uniform distribution. Using convincing heuristic arguments, the conditional probability distributions of the size of the largest prime factor p 1 (n) of a number n on the order of N is derived, given that n satisses one of the conditions 2n+1 is prime, ...

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the assumption that the probability generating function of the claim size be algebraic. The probability generating function of the claim number is supposed to b...