“On the Use of Some Variation Distance Inequalities to Estimate the Difference between Sample and Perturbed Sample”

Author(s):  
A. Hillion
1996 ◽  
Vol 33 (2) ◽  
pp. 472-489 ◽  
Author(s):  
A. D. Barbour ◽  
Timothy C. Brown

In 1979, Melamed proved that, in an open migration process, the absence of ‘loops' is necessary and sufficient for the equilibrium flow along a link to be a Poisson process. In this paper, we prove approximation theorems with the same flavour: the difference between the equilibrium flow along a link and a Poisson process with the same rate is bounded in terms of expected numbers of loops. The proofs are based on Stein's method, as adapted for bounds on the distance of the distribution of a point process from a Poisson process in Barbour and Brown (1992b). Three different distances are considered, and illustrated with an example consisting of a system of tandem queues with feedback. The upper bound on the total variation distance of the process grows linearly with time, and a lower bound shows that this can be the correct order of approximation.


2018 ◽  
Vol 33 (2) ◽  
pp. 186-204 ◽  
Author(s):  
Jianping Yang ◽  
Wanwan Xia ◽  
Taizhong Hu

The relation between extropy and variational distance is studied in this paper. We determine the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution, obtain the tightest upper bound on the difference of extropies of any two probability distributions subject to the variational distance constraint, and establish an analytic formula for the confidence interval of an extropy. Such a study parallels to that of Ho and Yeung [3] concerning entropy. However, the proofs of the main results in this paper are different from those in Ho and Yeung [3]. In fact, our arguments can simplify several proofs in Ho and Yeung [3].


Author(s):  
Mehrdad Valizadeh ◽  
Amin Gohari

We provide a new tool for simulation of a random variable (target source) from a randomness source with side information. Considering the total variation distance as the measure of precision, this tool offers an upper bound for the precision of simulation, which is vanishing exponentially in the difference of Rényi entropies of the randomness and target sources. This tool finds application in games in which the players wish to generate their actions (target source) as a function of a randomness source such that they are almost independent of the observations of the opponent (side information). In particular, we study zero-sum repeated games in which the players are restricted to strategies that require only a limited amount of randomness. Let be the max-min value of the n stage game. Previous works have characterized [Formula: see text], that is, the long-run max-min value, but they have not provided any result on the value of vn for a given finite n-stage game. Here, we utilize our new tool to study how vn converges to the long-run max-min value.


2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Tamás F. Móri

The paper is a contribution to the problem of estimating the deviation of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [0,1]. Deviation can be measured by the difference of the kth terms or by total variation distance. Our new bounds have better order of magnitude than those proved previously, and they are even sharp in certain cases.


1996 ◽  
Vol 33 (02) ◽  
pp. 472-489 ◽  
Author(s):  
A. D. Barbour ◽  
Timothy C. Brown

In 1979, Melamed proved that, in an open migration process, the absence of ‘loops' is necessary and sufficient for the equilibrium flow along a link to be a Poisson process. In this paper, we prove approximation theorems with the same flavour: the difference between the equilibrium flow along a link and a Poisson process with the same rate is bounded in terms of expected numbers of loops. The proofs are based on Stein's method, as adapted for bounds on the distance of the distribution of a point process from a Poisson process in Barbour and Brown (1992b). Three different distances are considered, and illustrated with an example consisting of a system of tandem queues with feedback. The upper bound on the total variation distance of the process grows linearly with time, and a lower bound shows that this can be the correct order of approximation.


2019 ◽  
Vol 2 (2) ◽  
pp. 53
Author(s):  
Lutfi Ahmad Yudandi ◽  
Bambang Setiawan ◽  
Noegroho Djarwanti

<em>Soft soil has low bearing capacity and high compressibility that can cause instability and long-term degradation that can make around some road settlement or wavy. A solution to prevent this soft soil problem was built Modified Chicken Foot, The function of Chicken Foot Foundation is to increase its bearing capacity. This research is using single load<strong> </strong>with variation distance of triangle foot foundation pattern whereas analysis of deflection using finite element method based. The research shows displacement result is depend on distance between load position and foot foundation, the closer distance between foot foundation the less it would result. The displacement result that happened at roadside is larger than at middle of the road, the difference between them is -6,8% up to 67% and The displacement result that happened in plate without pipe is larger than a plate with pipe, the difference between them is 12,31% up to 59,41%.  </em>


2018 ◽  
Author(s):  
Andrew Melfi ◽  
Divakar Viswanath

AbstractThe first terms of the Wright-Fisher (WF) site frequency spectrum that follow the coalescent approximation are determined precisely, with a view to understanding the accuracy of the coalescent approximation for large samples. The perturbing terms show that the probability of a single mutant in the sample (singleton probability) is elevated in WF but the rest of the frequency spectrum is lowered. A part of the perturbation can be attributed to a mismatch in rates of merger between WF and the coalescent. The rest of it can be attributed to the difference in the way WF and the coalescent partition children between parents. In particular, the number of children of a parent is approximately Poisson under WF and approximately geometric under the coalescent. Whereas the mismatch in rates raises the probability of singletons under WF, its offspring distribution being approximately Poisson lowers it. The two effects are of opposite sense everywhere except at the tail of the frequency spectrum. The WF frequency spectrum begins to depart from that of the coalescent only for sample sizes that are comparable to the population size. These conclusions are confirmed by a separate analysis that assumes the sample size n to be equal to the population size N. Partly thanks to the canceling effects, the total variation distance of WF minus coalescent is 0.12/ log N for a population sized sample with n = N, which is only 1% for N = 2 × 104.


1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.


1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall

AbstractThe oldest cell-like structures on Earth are preserved in silicified lagoonal, shallow sea or hydrothermal sediments, such as some Archean formations in Western Australia and South Africa. Previous studies concentrated on the search for organic fossils in Archean rocks. Observations of silicified bacteria (as silica minerals) are scarce for both the Precambrian and the Phanerozoic, but reports of mineral bacteria finds, in general, are increasing. The problems associated with the identification of authentic fossil bacteria and, if possible, closer identification of bacteria type can, in part, be overcome by experimental fossilisation studies. These have shown that not all bacteria fossilise in the same way and, indeed, some seem to be very resistent to fossilisation. This paper deals with a transmission electron microscope investigation of the silicification of four species of bacteria commonly found in the environment. The Gram positiveBacillus laterosporusand its spore produced a robust, durable crust upon silicification, whereas the Gram negativePseudomonas fluorescens, Ps. vesicularis, andPs. acidovoranspresented delicately preserved walls. The greater amount of peptidoglycan, containing abundant metal cation binding sites, in the cell wall of the Gram positive bacterium, probably accounts for the difference in the mode of fossilisation. The Gram positive bacteria are, therefore, probably most likely to be preserved in the terrestrial and extraterrestrial rock record.


1994 ◽  
Vol 144 ◽  
pp. 421-426
Author(s):  
N. F. Tyagun

AbstractThe interrelationship of half-widths and intensities for the red, green and yellow lines is considered. This is a direct relationship for the green and yellow line and an inverse one for the red line. The difference in the relationships of half-widths and intensities for different lines appears to be due to substantially dissimilar structuring and to a set of line-of-sight motions in ”hot“ and ”cold“ corona regions.When diagnosing the coronal plasma, one cannot neglect the filling factor - each line has such a factor of its own.


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