Estimation of the Error of the Method of Statistical Tests (Monte-Carlo) Due to Imperfections in the Distribution of Random Numbers

1973 ◽  
Vol 17 (3) ◽  
pp. 493-509 ◽  
Author(s):  
G. A. Kozlov
Keyword(s):  
Monte Carlo ◽  
Statistical Tests ◽  
Random Numbers

Random-Number Generation

1991 ◽  
Vol 02 (01) ◽  
pp. 296-299
Author(s):  
A. COMPAGNER
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Large Scale ◽  
Random Number ◽  
Statistical Tests ◽  
Random Number Generation ◽  
Operational Definition ◽  
Random Numbers ◽  
The Many ◽  
Definition Of

In large-scale Monte Carlo simulations, reliable random numbers will soon be needed at bit rates of 1 GHz or more. Therefore, existing recipes for the generation of random numbers have to be improved. This is not easy, due to the many unrelated and laborious statistical tests needed to compensate for the lack of an accepted and operational definition of randomness. When however the notion of randomness as a complete absence of all correlations is made precise, a practical approach results.

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

Multilevel Monte Carlo by using the Halton sequence

2020 ◽  
Vol 26 (3) ◽  
pp. 193-203
Author(s):  
Shady Ahmed Nagy ◽  
Mohamed A. El-Beltagy ◽  
Mohamed Wafa
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Computational Cost ◽  
Random Numbers ◽  
Multilevel Monte Carlo ◽  
Halton Sequence ◽  
Random Generator ◽  
Mc Simulation ◽  
Multilevel Monte Carlo Method

AbstractMonte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

scholarly journals New Statistical Randomness Tests Based on Length of Runs

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Ali Doğanaksoy ◽  
Fatih Sulak ◽  
Muhiddin Uğuz ◽  
Okan Şeker ◽  
Ziya Akcengiz
Keyword(s):  
Statistical Tests ◽  
Random Sequence ◽  
Cryptographic Protocols ◽  
Experimental Results ◽  
Security Evaluation ◽  
Random Numbers ◽  
Statistical Distributions ◽  
Cryptographic Algorithm ◽  
Encryption Algorithms ◽  
Randomness Tests

Random sequences and random numbers constitute a necessary part of cryptography. Many cryptographic protocols depend on random values. Randomness is measured by statistical tests and hence security evaluation of a cryptographic algorithm deeply depends on statistical randomness tests. In this work we focus on statistical distributions of runs of lengths one, two, and three. Using these distributions we state three new statistical randomness tests. New tests useχ2distribution and, therefore, exact values of probabilities are needed. Probabilities associated runs of lengths one, two, and three are stated. Corresponding probabilities are divided into five subintervals of equal probabilities. Accordingly, three new statistical tests are defined and pseudocodes for these new statistical tests are given. New statistical tests are designed to detect the deviations in the number of runs of various lengths from a random sequence. Together with some other statistical tests, we analyse our tests’ results on outputs of well-known encryption algorithms and on binary expansions ofe,π, and2. Experimental results show the performance and sensitivity of our tests.

Statistical tests of differential susceptibility: Performance, limitations, and improvements

2017 ◽  
Vol 29 (4) ◽  
pp. 1267-1278 ◽  
Author(s):  
Marco Del Giudice
Keyword(s):  
Monte Carlo ◽  
Statistical Approach ◽  
Statistical Tests ◽  
Differential Susceptibility ◽  
Initial Response ◽  
Empirical Literature ◽  
False Negatives ◽  
Interaction Index ◽  
Future Studies ◽  
Highly Sensitive

AbstractStatistical tests of differential susceptibility have become standard in the empirical literature, and are routinely used to adjudicate between alternative developmental hypotheses. However, their performance and limitations have never been systematically investigated. In this paper I employ Monte Carlo simulations to explore the functioning of three commonly used tests proposed by Roisman et al. (2012). Simulations showed that critical tests of differential susceptibility require considerably larger samples than standard power calculations would suggest. The results also showed that existing criteria for differential susceptibility based on the proportion of interaction index (i.e., values between .40 and .60) are especially likely to produce false negatives and highly sensitive to assumptions about interaction symmetry. As an initial response to these problems, I propose a revised test based on a broader window of proportion of interaction index values (between .20 and .80). Additional simulations showed that the revised test outperforms existing tests of differential susceptibility, considerably improving detection with little effect on the rate of false positives. I conclude by noting the limitations of a purely statistical approach to differential susceptibility, and discussing the implications of the present results for the interpretation of published findings and the design of future studies in this area.

scholarly journals Enhancing the operational efficiency of quantum random number generators

2021 ◽  
Vol 13 (2) ◽  
pp. 10-18
Author(s):  
Botond L. Márton ◽  
Dóra Istenes ◽  
László Bacsárdi
Keyword(s):  
Random Number ◽  
Statistical Tests ◽  
Practical Implementation ◽  
Random Numbers ◽  
Random Number Generators ◽  
Original Source ◽  
Negative Effect ◽  
Quantum Phenomena ◽  
The Right

Random numbers are of vital importance in today’s world and used for example in many cryptographical protocols to secure the communication over the internet. The generators producing these numbers are Pseudo Random Number Generators (PRNGs) or True Random Number Generators (TRNGs). A subclass of TRNGs are the Quantum based Random Number Generators (QRNGs) whose generation processes are based on quantum phenomena. However, the achievable quality of the numbers generated from a practical implementation can differ from the theoretically possible. To ease this negative effect post-processing can be used, which contains the use of extractors. They extract as much entropy as possible from the original source and produce a new output with better properties. The quality and the different properties of a given output can be measured with the help of statistical tests. In our work we examined the effect of different extractors on two QRNG outputs and found that witg the right extractor we can improve their quality.

scholarly journals Prediksi Tingkat Penerimaan Lulusan Siswa Kejuruan dalam Dunia Usaha dan Industri Menggunakan Metode Monte Carlo

2020 ◽  
pp. 84-89
Author(s):  
Hasanatul Iftitah ◽  
Y Yuhandri
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Prediction Accuracy ◽  
Vocational School ◽  
Vocational Schools ◽  
Random Numbers ◽  
Vocational High School ◽  
The Monte Carlo Method ◽  
Academic Year

Vocational High School (SMK) Negeri 4 Kota Jambi is one of the favorite vocational schools in Jambi City which is also the only pure tourism vocational school in Jambi Province. SMK Negeri 4 Kota Jambi has several vocational majors, namely culinary, beauty, fashion and hospitality. In general, students who choose to attend vocational schools have the hope of being able to work immediately after graduating from school, they do not need to continue to study to be able to work. In this study, researchers will predict the level of acceptance of students from SMK Negeri 4 Kota Jambi in the business and industrial world using the Monte Carlo method. Monte Carlo is a method that can find values ​​that are close to the actual value of events that will occur based on the distribution of sampling data. The technique of this method is to select random numbers from the probability distribution to perform the simulation. The data used in this study is the data of students from SMK Negeri 4 Kota Jambi who worked from the 2015/2016 Academic Year to the 2018/2019 Academic Year. Furthermore, the data will be processed using the Monte Carlo method. The simulation will be implemented using PHP programming. The result of this research is the level of prediction accuracy of students of SMK Negeri 4 Kota Jambi who are accepted in the business and industrial world using the Monte Carlo method is 84%.

Sign in / Sign up

Export Citation Format

Share Document