Random Number Generation and Monte Carlo Methods

doi:10.1007/b97336

Cited by 13 publications

(7 citation statements)

References 297 publications

(373 reference statements)

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“…The Monte Carlo method provides approximate numerical solutions to various problems by performing statistical sampling experiments on a computer. The method is especially useful for mathematical problems which are too complicated to solve analytically [11,12,17].…”

Section: The Monte Carlo Methodsmentioning

confidence: 99%

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The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison between the Classical Approach and the Monte Carlo Method

Danković

Antić

Nikolić

et al. 2017

ITC

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This paper presents the stability analysis of the linear recursive (prediction) filters with higher-order predictors in a DPCM (differential pulse-code modulation) system, where traditional methods become too difficult and complex. Stability conditions for the third-and fourth-order predictor are given by using the Schur-Cohn stability criterion. The probability of stability estimation is performed by using the Monte Carlo method. Verification of the proposed method is performed for lower-order predictors (the first-and second-order). We calculated numerical values of the probability of stability for higher-order predictors and previously experimentally obtained parameters. With large enough number of trials (samples) in Monte Carlo simulation, we reach the desired accuracy.

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Section: The Monte Carlo Methodsmentioning

confidence: 99%

“…Despite some attempts, only theoretical approach of stability analysis for higher-order prediction filters has been given till now without adequate numerical results [5,23]. In this paper we use the Monte Carlo method [11,12] for numerical integration.…”

Section: Introductionmentioning

confidence: 99%

The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison between the Classical Approach and the Monte Carlo Method

Danković

Antić

Nikolić

et al. 2017

ITC

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“…From the data base of number of cases of ATL, the monthly probabilistic frequency was estimated and the cumulative probability mass distribution was obtained. So a partition interval (0,1) could be establish, then following two steps a random number X will be generated from probability mass function p: first generate U ∼ U n(0, 1), and second determine the smallest positive integer I such that u ≤ F (x I ), and return X = x I [8]. In each year y i , the measure of the simulated samples was determined by the 1-norm vector of monthly cases, i.e.…”

Section: Modeling Method Simulation and Statistical Analysismentioning

confidence: 99%

Monte Carlo simulation of American Tegumentary Leishmaniasis epidemic. The case in Oran, Salta, Argentina, 1985-2007

Rosales¹,

Blas²,

Yang³

2017

ams

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The present study aimed to understanding some of the process underling in the dynamics of American Tegumentary Leishmaniasis (ATL), which had occurred in Department of Orán, Argentina, in the period 1985-2007. The monthly empirically estimations occurrence probabilities of cases of ATL could be to help understand how epidemiological mechanisms of enhancement during the endemic period or outbreaks of ATL. We have estimated monthly probabilities of occurrence thereof, the monthly empirical cumulative distribution function, the monthly probability mass function, in order to establish a partition of [0,1] and apply-

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“…Aside 7. Computers typically use pseudo-random number generators which have their own fascinating field (Gentle, 2003;Knuth, 1997).…”

Section: 2mentioning

confidence: 99%

Coin-Flipping, Ball-Dropping, and Grass-Hopping for Generating Random Graphs from Matrices of Edge Probabilities

Ramani¹,

Eikmeier²,

Gleich³

2019

SIAM Rev.

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Common models for random graphs, such as Erdős-Rényi and Kronecker graphs, correspond to generating random adjacency matrices where each entry is non-zero based on a large matrix of probabilities. Generating an instance of a random graph based on these models is easy, although inefficient, by flipping biased coins (i.e. sampling binomial random variables) for each possible edge. This process is inefficient because most large graph models correspond to sparse graphs where the vast majority of coin flips will result in no edges. We describe some not-entirely-well-known, but not-entirely-unknown, techniques that will enable us to sample a graph by finding only the coin flips that will produce edges. Our analogies for these procedures are ball-dropping, which is easier to implement, but may need extra work due to duplicate edges, and grass-hopping, which results in no duplicated work or extra edges. Grass-hopping does this using geometric random variables. In order to use this idea on complex probability matrices such as those in Kronecker graphs, we decompose the problem into three steps, each of which are independently useful computational primitives: (i) enumerating non-decreasing sequences, (ii) unranking multiset permutations, and (iii) decoding and encoding z-curve and Morton codes and permutations. The third step is the result of a new connection between repeated Kronecker product operations and Morton codes. Throughout, we draw connections to ideas underlying applied math and computer science including coupon collector problems.

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Random Number Generation and Monte Carlo Methods

Cited by 13 publications

References 297 publications

The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison between the Classical Approach and the Monte Carlo Method

The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison between the Classical Approach and the Monte Carlo Method

Monte Carlo simulation of American Tegumentary Leishmaniasis epidemic. The case in Oran, Salta, Argentina, 1985-2007

Coin-Flipping, Ball-Dropping, and Grass-Hopping for Generating Random Graphs from Matrices of Edge Probabilities

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