Showing papers on "Probability-generating function published in 1998"

Estimation in integer - valued moving average models

Abstract: The paper presents new characterizations of the integer-valued moving average model. For four model variants we give moments and probability generating functions. Yule-Walker and conditional least squares estimators are obtained and studied by Monte Carlo simulation. A new generalized method of moment estimator based on probability generating functions is presented and shown to be consistent and asymptotically normal.The small sample performance is in some instances better than those of alternative estimators. The techniques are illustrated on a time series of traded stocks.

Queues with hysteretic control by vacation and post-vacation periods

Abstract: The paper investigates the queueing process in stochastic systems with bulk input, batch state dependent service, server vacations, and three post-vacation disciplines. The policy of leaving and entering busy periods is hysteretic, meaning that, initially, the server leaves the system on multiple vacation trips whenever the queue falls below r (\geq1), and resumes service when during his absence the system replenishes to N or more customers upon one of his returns. During his vacation trips, the server can be called off on emergency, limiting his trips by a specified random variable (thereby encompassing several classes of vacation queues, such as ones with multiple and single vacations). If by then the queue has not reached another fixed treshold M (\leq N), the server enters a so-called “post-vacation period” characterized by three different disciplines: waiting, or leaving on multiple vacation trips with or without emergency. For all three disciplines, the probability generating functions of the discrete and continuous time parameter queueing processes in the steady state are obtained in a closed analytic form. The author uses a semi-regenerative approach and enhances fluctuation techniques (from his previous studies) preceding the analysis of queueing systems. Various examples demonstrate and discuss the results obtained.

Blind signal flattening using warping neural modules

Abstract: The aim of the paper is to present a new blind transformation algorithm which makes flat (uniform) the probability density function of a random process. The same algorithm allows us to find a uniform hashing map between a set of source symbols and a set of associated ones. As a transformation a non-linear flexible parametric function is used. Its parameters are continuously changed through time for maximizing the entropy of the transformed random process. In a neural context, such a function will represent the input-output mapping performed by a single neuron endowed with functional links.

Queue length performance of some non-exhaustive polling models with Bernoulli feedback

Abstract: We study the queue length performance in non-exhaustive asymmetric polling systems with Bernoulli feedback. We obtain the PGF (probability generating functions) and the mean values of the queue lengths. For the gated polling model we define two new service policies: departure-gated policy and service-gated policy, and we demonstrate their difference in queueing performance. In an asymmetric system, the departure-gated policy is better than the service-gated policy. In a symmetric system however, these two non-exhaustive policies are not as good as an exhaustive policy. We also observe that the performance of 1-limited system degrading faster as the load increases.

Using generator function system to check independence of random variables

Abstract: This study presents a criterion to determine the stochastic dependence or independence between the variables of a random vector or between two of its subvectors, either from the joint density function or from the generator function system for such a density. This criterion generalizes the condition discussed by HERRERIAS R., PALACIOS F. and CALLEJON J.(1997). There is a noteworthy simplicity of calculations, as the stochastic dependence or independence of random variables is seen as a consequence of the analytical dependence or independence in the generator function system.

Estimation in integer - valued moving average models

Abstract: The paper presents new characterizations of the integer-valued moving average model. For four model variants we give moments and probability generating functions. Yule-Walker and conditional least squares estimators are obtained and studied by Monte Carlo simulation. A new generalized method of moment estimator based on probability generating functions is presented and shown to be consistent and asymptotically normal.The small sample performance is in some instances better than those of alternative estimators. The techniques are illustrated on a time series of traded stocks.

New Approximation Approach for Stochastic Programming Problems with Probability Function

Abstract: Many practical problems can be formalized as optimization problems with a probability function in its objective or in constraints. But only for linear cases the optimization technique is well developed for solving these problems [2, 3, 6]. Generally, difficulties arise since we can not represent the probability function analytically or in the form of expectation of a smooth function. In [1, 2, 3, 6, 7, 8] numerical methods based on some estimations of the probability function and its gradient are suggested. Most of them have low convergence rate because they need expensive calculations for estimating the probability function and its gradient at every point.

A probabilistic proof ofthe series representation of the macdonald function with applications

Abstract: A series representation of the Macdonald function is obtained using the properties of a probability density function and its moment generating function. Some applications of the result are discussed and an open problem is posed.