In this paper,by making use of Divergence theorem for multiple integrals,we establish some integral inequalities for schur convex functions defined on bodies B⊂R^(n)that are symmetric,convex and have nonempty *** for ...
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In this paper,by making use of Divergence theorem for multiple integrals,we establish some integral inequalities for schur convex functions defined on bodies B⊂R^(n)that are symmetric,convex and have nonempty *** for three dimensional balls are also provided.
The introduction of shape parameters into statistical distributions provided flexible models that produced better fit to experimental data. The Weibull and gamma families are prime examples wherein shape parameters pr...
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The introduction of shape parameters into statistical distributions provided flexible models that produced better fit to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many independent gamma populations, one may test equality (or homogeneity) of shape parameters. In this article, we develop two tests for testing shape parameters of gamma distributions using chi-square distributions, stochastic majorization, and schurconvexity. The first one tests hypotheses on the shape parameter of a single gamma distribution. We numerically examine the performance of this test and find that it controls Type I error rate for small samples. To compare shape parameters of a set of independent gamma populations, we develop a test that is unbiased in the sense of schurconvexity. These tests are motivated by the need to have simple, easy to use tests and accurate procedures in case of small samples. We illustrate the new tests using three real datasets taken from engineering and environmental science. In addition, we investigate the Bayes' factor in this context and conclude that for small samples, the frequentist approach performs better than the Bayesian approach.
Correlations are a source of continuing discoveries. A new inequality is obtained that provides easily computed bounds for the determinant of a correlation matrix. (C) 2014 Elsevier B.V. All rights reserved.
Correlations are a source of continuing discoveries. A new inequality is obtained that provides easily computed bounds for the determinant of a correlation matrix. (C) 2014 Elsevier B.V. All rights reserved.
Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk ...
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Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk has to be taken into consideration. On the other hand the premium that the insured pays has to be fair. This fairness is measured by a function of the difference between the risk and the premium paid-we call this function a distance function. For a given small probability of insolvency, we find the premium for each class, such that the distance function is minimized. Next we formulate and solve the dual problem, which is minimizing the insolvency probability under the constraint that the distance function does not exceed a given level. This paper generalizes a previous paper [Zaks, Y., Frostig, E., Levikson, B., 2006. Optimal pricing of a heterogeneous portfolio for a given risk level. Astin Bull. 36 (1), 161-185] where only a square distance function was considered. (c) 2006 Elsevier B.V. All rights reserved.
The usage of multichannel receivers that are followed by diversity combining can significantly improve the performance of wireless communications links. In this paper, we investigate in some detail three popular techn...
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The usage of multichannel receivers that are followed by diversity combining can significantly improve the performance of wireless communications links. In this paper, we investigate in some detail three popular techniques for diversity combining, namely maximal ratio combining (MRC), equal gain combining, and selection combining. The main goal is to investigate under which circumstances it can be guaranteed that a certain technique does indeed decrease the probability of error of a multichannel receiver. The analyzed fading model is quite general with the only assumption that fading gains are scaled exchangeable random variables. The crucial mathematical tool used to produce the results of this paper is the powerful theory of stochastic majorization. Among other results, it was shown that the average bit-error probability of the MRC receiver with equally distributed average powers always decreases with the addition of a new diversity branch if the total power is fixed.
We show that the space of all binary Huffman codes for a finite alphabet defines a lattice, ordered by the imbalance of the code trees. Representing code trees as path-length sequences, we show that the imbalance orde...
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We show that the space of all binary Huffman codes for a finite alphabet defines a lattice, ordered by the imbalance of the code trees. Representing code trees as path-length sequences, we show that the imbalance ordering is closely related to a majorization ordering on real-valued sequences that correspond to discrete probability density functions. Furthermore, this tree imbalance is a partial ordering that is consistent with the total orderings given by either the external path length (sum of tree path lengths) or the entropy determined by the tree structure. On the imbalance lattice, we show the weighted path-length of a tree (the usual objective function for Huffman coding) is a submodular function, as is the corresponding function on the majorization lattice. Submodular functions are discrete analogues of convexfunctions. These results give perspective on Huffman coding and suggest new approaches to coding as optimization over a lattice.
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