Topic
Probability-generating function
About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.
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01 Jan 2005
TL;DR: The behavior of a discrete-time multiserver buffer system with infinite buffer size is investigated by means of an analytical technique based on probability generating functions (pgf’s), and the moments and the tail distributions of the system contents and the packet delay are calculated.
Abstract: We investigate the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive at the system according to a two-state correlated arrival process. The service times of the packets are assumed to be constant, equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating functions (pgf’s). Explicit expressions are obtained for the pgf’s of the system contents and the packet delay. From these, the moments and the tail distributions of the system contents and the packet delay can be calculated. Numerical examples are given to show the influence of various model parameters on the system behavior.
2 citations
TL;DR: In this paper, the authors give conditions for such a mixing scheme to exist and a functional law of large numbers for E (1n X ) is used to prove that mixing or migration from each process occurs after each generation.
Abstract: The populations of critical and subcritical branching processes in random environments die out with probability one. But the total population of several such processes in which the sequences of environmental probability generating functions are independent, but mixing or migration from each process occurs after each generation, may be equivalent to the population of a supercritical branching process in random environments, which will survive with positive probability. This paper gives conditions for such a mixing scheme to exist. A functional law of large numbers for E (1n X ) is used.
2 citations
TL;DR: In this article, it was shown that the extremal distribution exists, is unique, and is necessarily an element of a certain subclass of the class of all (k + 1)-point distributions.
Abstract: Consider the set of proper probability distributions on the nonnegative integers having the first k moments (fixed) in common. It is desired to find the element of this set whose corresponding probability generating function (p.g.f.) lies entirely above or below the others. Using convexity arguments, it is shown that the extremal distribution exists, is unique, and is necessarily an element of a certain subclass of the class of all (k + 1)-point distributions. This subclass is entirely characterized by the geometrical properties of its set of support. The alternation of upper and lower bounds with the parity of k is also explained. There is mention of how the techniques developed here apply to more general discrete optimization problems, and the connection with the theory of cyclic polytopes is also discussed.
2 citations
01 Apr 2015
TL;DR: This paper describes several frequently used methods for generation and optimization of the designs and compares them using several basic function simulations.
Abstract: Nowadays, computer experiments are often used for evaluation of functions with random inputs. Instead of accessing a complex function and calculating the probability distribution function of the result, a set of computer simulations may be processed and the information concerning the properties of the resulting variable/random vector can be estimated. The quality of such an estimate depends on the number of simulations and also on the distribution of points in the sampling space. Since the time required for the calculation is proportional to the number of the design points, it is desirable to reduce this number while keeping the quality of the design. This can be achieved by appropriate selection of the design points (specific combinations of values of input variables out of the permissible range of values given by the probability distribution of each variable).This paper describes several frequently used methods for generation and optimization of the designs and compares them using several basic function...
2 citations
Journal Article•
TL;DR: In this paper, the gap probability at the hard and soft edges of scaled random matrix ensembles with orthogonal symmetry is known in terms of τ -functions, and their generalizations to contain a generating function parameter, can be expressed as Fredholm determinants.
Abstract: The gap probability at the hard and soft edges of scaled random matrix ensembles with orthogonal symmetry are known in terms of τ -functions. Extending recent work relating to the soft edge, it is shown that these τ -functions, and their generalizations to contain a generating function parameter, can be expressed as Fredholm determinants. These same Fredholm determinants occur in exact expressions for the same gap probabilities in scaled random matrix ensembles with unitary and symplectic symmetry.
2 citations