Twister Generator of Poisson Random Numbers with the Use of Cumulative Frequency Technology

2020 ◽  
pp. 101-123
Author(s):  
A.F. Deon ◽  
D.D. Dmitriev ◽  
Yu.A. Menyaev
Keyword(s):  
Poisson Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Convergence In Probability ◽  
Random Numbers ◽  
Cumulative Frequency ◽  
New Approach ◽  
Frequency Distributions ◽  
Simulation Results

The widely known generators of Poisson random variables are associated with different modifications of the algorithm based on the convergence in probability of a sequence of uniform random variables to the created stochastic number. However, in some situations, this approach yields different discrete Poisson probability distributions and skipping in the generated numbers. This paper offers a new approach for creating Poisson random variables based on the complete twister generator of uniform random variables, using cumulative frequency technology. The simulation results confirm that probabilistic and frequency distributions of the obtained stochastic numbers completely coincide with the theoretical Poisson distribution. Moreover, combining this new approach with the tuning algorithm of basic twister generation allows for a significant increase in length of the created sequences without using additional RAM of the computer

scholarly journals Poisson Twister Generator by Cumulative Frequency Technology

Algorithms ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 114 ◽  
Author(s):  
Aleksei F. Deon ◽  
Yulian A. Menyaev
Keyword(s):  
Poisson Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Convergence In Probability ◽  
Cumulative Frequency ◽  
New Approach ◽  
Frequency Distributions ◽  
Simulation Results

The widely known generators of Poisson random variables are associated with different modifications of the algorithm based on the convergence in probability of a sequence of uniform random variables to the created stochastic number. However, in some situations, this approach yields different discrete Poisson probability distributions and skipping in the generated numbers. This article offers a new approach for creating Poisson random variables based on the complete twister generator of uniform random variables, using cumulative frequency technology. The simulation results confirm that probabilistic and frequency distributions of the obtained stochastic numbers completely coincide with the theoretical Poisson distribution. Moreover, combining this new approach with the tuning algorithm of basic twister generation allows for a significant increase in length of the created sequences without using additional RAM of the computer.

Continuous Random Numbers

2019 ◽  
pp. 54-69
Author(s):  
Robert H. Swendsen
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Delta Function ◽  
Ideal Gas ◽  
Dirac Delta Function ◽  
Bayesian Probability ◽  
Random Numbers ◽  
Continuous Variables ◽  
Dirac Delta ◽  
Discrete Random Variables

The theory of probability developed in Chapter 3 for discrete random variables is extended to probability distributions, in order to treat the continuous momentum variables. The Dirac delta function is introduced as a convenient tool to transform continuous random variables, in analogy with the use of the Kronecker delta for discrete random variables. The properties of the Dirac delta function that are needed in statistical mechanics are presented and explained. The addition of two continuous random numbers is given as a simple example. An application of Bayesian probability is given to illustrate its significance. However, the components of the momenta of the particles in an ideal gas are continuous variables.

scholarly journals Phase Congruential White Noise Generator

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 118
Author(s):  
Aleksei Deon ◽  
Oleg Karaduta ◽  
Yulian Menyaev
Keyword(s):  
White Noise ◽  
Random Variables ◽  
Noise Generator ◽  
Signal Generator ◽  
White Noise Process ◽  
New Approach ◽  
Noise Process ◽  
White Noise Generator ◽  
Phase Signal ◽  
Simulation Results

White noise generators can use uniform random sequences as a basis. However, such a technology may lead to deficient results if the original sequences have insufficient uniformity or omissions of random variables. This article offers a new approach for creating a phase signal generator with an improved matrix of autocorrelation coefficients. As a result, the generated signals of the white noise process have absolutely uniform intensities at the eigen Fourier frequencies. The simulation results confirm that the received signals have an adequate approximation of uniform white noise.

scholarly journals On the Dispersive Ordering and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Tran Loc Hung ◽  
Nguyen Van Son
Keyword(s):  
Unbiased Estimator ◽  
Probability Distributions ◽  
Random Variables ◽  
New Approach ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Dispersive Ordering

The purpose of this paper is to present some results related to the dispersive ordering of probability distributions via dispersion functions of the ℒ1-random variables. A new approach to the Laws of Large Numbers in ℒ1-norm can be applied via received results. A new concept on minimum-dispersive unbiased estimator is considered, too.

scholarly journals Simulasi Monte Carlo dalam Mengidentifikasi Peningkatan Penjualan Tanaman Mawar (Studi Kasus di Toko Bunga 5 Bersaudara Kota Solok)

2020 ◽  
Author(s):  
Dian Cyntia Dewi ◽  
S Sumijan ◽  
Gunadi Widi Nurcahyo
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Monte Carlo Simulations ◽  
Random Numbers ◽  
Cumulative Frequency ◽  
Simulation Process ◽  
The Monte Carlo Method ◽  
Simulation Results

Roses are one of the most popular types of plants in the community. The sale of roses at the flower shop of 5 siblings is increasingly in demand. Identifying the increase in sales is important in analyzing sales progress. At the present time the seller can only see a manual increase in sales that are most in demand. This study aims to determine predictions of the increase in sales of rose flowers with a monte carlo simulation accurately and accurately. The data that will be processed in this study in the last 2 years, namely 2018 and 2019, rose plants obtained at the 5 Brothers Flower Shop in Solok City. There are several types of roses in the predicted sales level. Then the data will be converted into the probability distribution into cumulative frequency and followed by generating random numbers so that they can determine random numbers. Next, we will group the boundary intervals of the random numbers that have been obtained and continue with the simulation process so that the simulation results and percentage accuracy are obtained using the Monte Carlo method. The results of this study on data processing from 2019 to 2020 have an accuracy of 90%. So this research is very appropriate in identifying the increase in sales for the following year. The design of this system determines the amount of increased sales of goods using the monte carlo method in a flower shop of 5 siblings. Monte Carlo simulations can be used to identify specific sales increases. The results obtained are quite accurate using the Monte Carlo method.

scholarly journals Calibration of numerical models based on advanced optimization and penalization techniques

2017 ◽  
Vol 68 (5) ◽  
pp. 396-400
Author(s):  
Pavel Karban ◽  
David Pánek ◽  
František Mach ◽  
Ivo Doležel
Keyword(s):  
Boundary Conditions ◽  
Numerical Models ◽  
Probability Distributions ◽  
Random Variables ◽  
Measured Data ◽  
Optimization Techniques ◽  
Physical Models ◽  
New Approach ◽  
Material Parameters ◽  
Normal Probability

Abstract A new approach to estimation of unknown material parameters and boundary conditions of physical models was developed. The approach is based on processing measured data by advanced optimization techniques connected with penalization. The data are supposed to be in the form of random variables with normal probability distributions. Several examples were calculated proving the strength of the proposed algorithm.

A Stochastic Analysis of a Solar Heated and Cooled House

1981 ◽  
Vol 103 (2) ◽  
pp. 158-166 ◽  
Author(s):  
Wiwut Tanthapanichakoon ◽  
D. M. Himmelblau
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Analysis ◽  
Probability Distributions ◽  
Random Variables ◽  
Frequency Distributions ◽  
Simulation Techniques ◽  
Standard Deviations ◽  
Model Equations ◽  
Stochastic Responses

Monte Carlo simulation techniques have been used to characterize the stochastic responses of the components of a solar heated and cooled house. Random variables with specified ensemble means, standard deviations, and probability distributions were introduced as inputs and parameters into the model equations for the house, and the equations solved repeatedly to provide samples of the component outputs. The character of the frequency distributions of the outputs, their means and standard deviations, and time statistics are discussed as well as implications with respect to the design of similar systems.

scholarly journals Some Information Geometric Aspects of Cyber Security by Face Recognition

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 878
Author(s):  
C. T. J. Dodson ◽  
John Soldera ◽  
Jacob Scharcanski
Keyword(s):  
Face Recognition ◽  
Cyber Security ◽  
Probability Distributions ◽  
Geodesic Distance ◽  
Recognition Method ◽  
Frequency Distributions ◽  
Face Images ◽  
User Access ◽  
Multidimensional Methods ◽  
Joint Probabilities

Secure user access to devices and datasets is widely enabled by fingerprint or face recognition. Organization of the necessarily large secure digital object datasets, with objects having content that may consist of images, text, video or audio, involves efficient classification and feature retrieval processing. This usually will require multidimensional methods applicable to data that is represented through a family of probability distributions. Then information geometry is an appropriate context in which to provide for such analytic work, whether with maximum likelihood fitted distributions or empirical frequency distributions. The important provision is of a natural geometric measure structure on families of probability distributions by representing them as Riemannian manifolds. Then the distributions are points lying in this geometrical manifold, different features can be identified and dissimilarities computed, so that neighbourhoods of objects nearby a given example object can be constructed. This can reveal clustering and projections onto smaller eigen-subspaces which can make comparisons easier to interpret. Geodesic distances can be used as a natural dissimilarity metric applied over data described by probability distributions. Exploring this property, we propose a new face recognition method which scores dissimilarities between face images by multiplying geodesic distance approximations between 3-variate RGB Gaussians representative of colour face images, and also obtaining joint probabilities. The experimental results show that this new method is more successful in recognition rates than published comparative state-of-the-art methods.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

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