On Taylor series expansions for waiting times in tandem queues: an algorithm for calculating the coefficients and an investigation of the approximation error

1999 ◽  
Vol 38 (3-4) ◽  
pp. 153-173 ◽  
Author(s):  
Wilfried Seidel ◽  
Kai v. Kocemba ◽  
Klaus Mitreiter
Keyword(s):  
Taylor Series ◽  
Waiting Times ◽  
Approximation Error ◽  
Series Expansions ◽  
Tandem Queues ◽  
Taylor Series Expansions

scholarly journals A Shortcut to LAD Estimator Asymptotics

1991 ◽  
Vol 7 (4) ◽  
pp. 450-463 ◽  
Author(s):  
P.C.B. Phillips
Keyword(s):  
Asymptotic Expansion ◽  
Regression Model ◽  
Taylor Series ◽  
Asymptotic Theory ◽  
Random Variables ◽  
Generalized Functions ◽  
Infinite Variance ◽  
Series Expansions ◽  
Linear Functionals ◽  
Taylor Series Expansions

Using generalized functions of random variables and generalized Taylor series expansions, we provide quick demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator.

scholarly journals A Method for the Generation of Various Ghost Correction Algorithms—the Example of the Positivity Method and the Exponential Method

1991 ◽  
Vol 13 (4) ◽  
pp. 199-212 ◽  
Author(s):  
P. Van Houtte
Keyword(s):  
Pole Figure ◽  
Taylor Series ◽  
The Other ◽  
New Method ◽  
Series Expansions ◽  
Theoretical Scheme ◽  
Taylor Series Expansions ◽  
Exponential Method ◽  
Pole Figure Data

A theoretical strategy is presented that can derive the algorithms of several existing ghost correction methods. The examples of the positivity method and the “GHOST” method are elaborated. A new method is derived as well: the “exponential” method. It can successfully replace the quadratic method as a method that yields an exactly non-negative complete C.O.D.F. from pole figure data. The theoretical scheme that can generate all these algorithms makes use of the fact, that several parameter sets can be defined in order to describe a C.O.D.F. The parameters of one set are then functions of those of the other. The algorithms are derived from Taylor series expansions of these functions.

scholarly journals Taylor series expansions for stationary Markov chains

2003 ◽  
Vol 35 (04) ◽  
pp. 1046-1070 ◽  
Author(s):  
Bernd Heidergott ◽  
Arie Hordijk
Keyword(s):  
Markov Chains ◽  
Taylor Series ◽  
Queueing System ◽  
Series Expansions ◽  
General State ◽  
Stationary Characteristic ◽  
Performance Function ◽  
Taylor Series Expansions ◽  
General State Space ◽  
Stationary Waiting Time

We study Taylor series expansions of stationary characteristics of general-state-space Markov chains. The elements of the Taylor series are explicitly calculated and a lower bound for the radius of convergence of the Taylor series is established. The analysis provided in this paper applies to the case where the stationary characteristic is given through an unbounded sample performance function such as the second moment of the stationary waiting time in a queueing system.

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