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Reexamining Discrete Approximations to Continuous Distributions
Decision Analysis, 2013Discretization is a common decision analysis technique for which many methods are described in the literature and employed in practice. The accuracy of these methods is typically judged by how well they match the mean, variance, and possibly higher moments of the underlying continuous probability distribution.
Robert K. Hammond, J. Eric Bickel
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Approximation of Discrete Sequential Boundaries
Biometrika, 1986Conservative critical limits for discrete sequential boundaries are derived, when the number of decision times and group sizes are not fixed in advance. The method at any stage of the sequential experiment requires only the joint distribution of the test statistics at the last two inspection times.
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An Approximate Algorithm for Discrete Linear Programming
IEEE Transactions on Systems Science and Cybernetics, 1969An algorithm is presented for determining an approximate solution of a large class of discrete linear programming problems, and an upper bound on the profit loss due to the approximation is computed. A subregion of the original polyhedron of feasible solutions is also defined; such a subregion certainly contains the optimal solution of the discrete ...
Emanuele Biondi, Roberto Schmid
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Discrete approximations to continuous curves
Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., 2006We consider the problem of approximating a continuous curve by a piecewise linear one whose segments are assumed to be connected by universal joints. Rather than taking a least-squares approach, we require that the endpoints of the line segments lie on the continuous curve.
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Note on Discrete Approximations
Journal of the American Statistical Association, 1973Abstract Suppose it is required to replace a continuous variate Z by an integer-valued approximation X in such a way that X retains as much information as possible. This problem is encountered, for example, in the field of educational measurement, where performance scores are often replaced by letter grades, which are then converted to grade points ...
W. Stefansky, Henry F. Kaiser
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Continuous and Discrete Approximations
2014In Chap. 10, we studied approximations using 2-norms that are defined from a dot product, and orthogonality was heavily used. In the first section of this chapter, we study polynomial approximation of continuous functions on an interval [a, b] using the uniform norm \(\|\cdot \|_{\infty }\).
Tom Lyche, Jean-Louis Merrien
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The Concepts of Discrete Convergence and Discrete Approximations
1985The concepts of discrete convergence and discrete approximation make the idea of approximating elements or spaces by sequences of elements or spaces more precise in a general setting. These concepts are introduced in Section 5.1, and explained by means of introductory examples.
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Discretized Normal Approximation
2011Returning to the independent case, and inspired by use of the continuity correction for the normal approximation of the binomial, Chap. 7 considers the approximation of independent sums of integer valued random variables by the discretized normal distribution, in the total variation metric.
Louis H. Y. Chen +2 more
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Discrete approximations of differential inclusions.
Summary: This paper is devoted to discretization methods for initial value problems for differential inclusions. The main emphasis is on set-valued analogues of Runge-Kutta methods. The material is presented as a survey, simultaneously containing a series of new results. Complete proofs are contained in our extended version [Bayreuther Math. Schr.Lempio, Frank, Veliov, Vladimir
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