scholarly journals BOUNDS FOR THE DISTRIBUTION OF TWO-DIMENSIONAL BINARY SCAN STATISTICS

2003 ◽  
Vol 17 (4) ◽  
pp. 509-525 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Markos V. Koutras
Keyword(s):  
Distribution Function ◽  
Present Article ◽  
Numerical Study ◽  
Double Sequence ◽  
Reliability Theory ◽  
Scan Statistics ◽  
Asymptotic Result ◽  
Two Dimensional ◽  
Scan Statistic ◽  
Binary Trials

In the present article, we develop some efficient bounds for the distribution function of a two-dimensional scan statistic defined on a (double) sequence of independent and identically distributed (i.i.d.) binary trials. The methodology employed here takes advantage of the connection between the scan statistic problem and an equivalent reliability structure and exploits appropriate techniques of reliability theory to establish tractable bounds for the distribution of the statistic of interest. An asymptotic result is established and a numerical study is carried out to investigate the efficiency of the suggested bounds.

New maximal inequalities for N-demimartingales with scan statistic applications

2017 ◽  
Vol 54 (2) ◽  
pp. 363-378 ◽  
Author(s):  
Markos V. Koutras ◽  
Demetrios P. Lyberopoulos
Keyword(s):  
Distribution Function ◽  
Waiting Time ◽  
Cumulative Distribution Function ◽  
Numerical Study ◽  
Cumulative Distribution ◽  
Scan Statistic ◽  
Maximal Inequalities ◽  
Binary Trials ◽  
First Occurrence ◽  
Independent And Identically Distributed

Abstract In the present work, some new maximal inequalities for nonnegative N-demi(super)martingales are first developed. As an application, new bounds for the cumulative distribution function of the waiting time for the first occurrence of a scan statistic in a sequence of independent and identically distributed (i.i.d.) binary trials are obtained. A numerical study is also carried out for investigating the behavior of the new bounds.

Large-deviation approximations to the distribution of scan statistics

1991 ◽  
Vol 23 (04) ◽  
pp. 751-771 ◽  
Author(s):  
Clive R. Loader
Keyword(s):  
Large Deviation ◽  
Two Dimensions ◽  
Unit Interval ◽  
Scan Statistics ◽  
Boundary Crossing ◽  
Two Dimensional ◽  
Likelihood Ratio Criterion ◽  
Scan Statistic ◽  
Window Width ◽  
Ratio Criterion

Suppose a Poisson process is observed on the unit interval. The scan statistic is defined as the maximum number of events observed as a window of fixed width is moved across the interval, and the distribution under homogeneity has been widely studied. Frequently, we may not wish to specify the window width in advance but to consider scan statistics with varying window widths. We propose a modification of the scan statistic based on a likelihood ratio criterion. This leads to a boundary-crossing problem for a two-dimensional random field, which we approximate using a large-deviation scaling under homogeneity. Similar results are obtained for Poisson processes observed in two dimensions. Numerical computations and simulations are used to illustrate the accuracy of the approximations.

scholarly journals Discrete Scan Statistics Generated by Exchangeable Binary Trials

2010 ◽  
Vol 47 (4) ◽  
pp. 1084-1092 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Closed Form ◽  
Random Variables ◽  
Random Variable ◽  
Scan Statistics ◽  
Bernoulli Trials ◽  
Scan Statistic ◽  
Binary Trials ◽  
Special Case ◽  
Independent Identically Distributed

Let {Xi}i=1n be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable Sn,m to be the maximum number of 1s within any m consecutive trials in {Xi}i=1n. The random variable Sn,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {Xi}i=1n consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of Sn,m for 2m ≥ n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.

Large-deviation approximations to the distribution of scan statistics

1991 ◽  
Vol 23 (4) ◽  
pp. 751-771 ◽  
Author(s):  
Clive R. Loader
Keyword(s):  
Large Deviation ◽  
Two Dimensions ◽  
Unit Interval ◽  
Scan Statistics ◽  
Boundary Crossing ◽  
Two Dimensional ◽  
Likelihood Ratio Criterion ◽  
Scan Statistic ◽  
Window Width ◽  
Ratio Criterion

Suppose a Poisson process is observed on the unit interval. The scan statistic is defined as the maximum number of events observed as a window of fixed width is moved across the interval, and the distribution under homogeneity has been widely studied. Frequently, we may not wish to specify the window width in advance but to consider scan statistics with varying window widths. We propose a modification of the scan statistic based on a likelihood ratio criterion. This leads to a boundary-crossing problem for a two-dimensional random field, which we approximate using a large-deviation scaling under homogeneity. Similar results are obtained for Poisson processes observed in two dimensions. Numerical computations and simulations are used to illustrate the accuracy of the approximations.

scholarly journals Discrete Scan Statistics Generated by Exchangeable Binary Trials

2010 ◽  
Vol 47 (04) ◽  
pp. 1084-1092 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Closed Form ◽  
Random Variables ◽  
Random Variable ◽  
Scan Statistics ◽  
Bernoulli Trials ◽  
Scan Statistic ◽  
Binary Trials ◽  
Special Case ◽  
Independent Identically Distributed

Let {X i } i=1 n be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S n,m to be the maximum number of 1s within any m consecutive trials in {X i } i=1 n . The random variable S n,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X i } i=1 n consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S n,m for 2m ≥ n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.

Numerical Study on Two-dimensional Magnetic Photonic Crystals Made of Magnetized Ferrites

PIERS Online ◽  
2007 ◽  
Vol 3 (3) ◽  
pp. 305-307 ◽  
Author(s):  
Jie Xu ◽  
Ping Chen ◽  
Yue Shi ◽  
Xin-Yi Ji ◽  
Ai-Min Jiang ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Numerical Study ◽  
Two Dimensional ◽  
Magnetic Photonic Crystals

Co-planar two-dimensional Metal-Insulator-Semiconductor Capacitor: Numerical study of the device electrostatics.

2017 ◽  
Author(s):  
Varun Bheemireddy
Keyword(s):  
Space Charge ◽  
High Performance ◽  
Numerical Study ◽  
2D Materials ◽  
Space Charge Density ◽  
Two Dimensional ◽  
Short Channel ◽  
Metal Insulator ◽  
Metal Insulator Semiconductor ◽  
New Family

The two-dimensional(2D) materials are highly promising candidates to realise elegant and e cient transistor. In the present letter, we conjecture a novel co-planar metal-insulator-semiconductor(MIS) device(capacitor) completely based on lateral 2D materials architecture and perform numerical study of the capacitor with a particular emphasis on its di erences with the conventional 3D MIS electrostatics. The space-charge density features a long charge-tail extending into the bulk of the semiconductor as opposed to the rapid decay in 3D capacitor. Equivalently, total space-charge and semiconductor capacitance densities are atleast an order of magnitude more in 2D semiconductor. In contrast to the bulk capacitor, expansion of maximum depletion width in 2D semiconductor is observed with increasing doping concentration due to lower electrostatic screening. The heuristic approach of performance analysis(2D vs 3D) for digital-logic transistor suggest higher ON-OFF current ratio in the long-channel limit even without third dimension and considerable room to maximise the performance of short-channel transistor. The present results could potentially trigger the exploration of new family of co-planar at transistors that could play a signi significant role in the future low-power and/or high performance electronics.<br>

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