scholarly journals On a Discrete Kolmogorov Criterion

2002 ◽  
Vol 114 (1) ◽  
pp. 141-146
Author(s):  
M. Finzel
Keyword(s):  
Kolmogorov Criterion

Mathematical-Statistical Methods for the Analysis of Aerial Triangulation Adjustment Errors Using a Computer Program

1975 ◽  
Vol 29 (2) ◽  
pp. 175-188
Author(s):  
M. Mosaad Allam
Keyword(s):  
Computer Program ◽  
Frequency Interval ◽  
Mean Square ◽  
Fisher Criterion ◽  
Statistical Parameters ◽  
Sample Distribution ◽  
Development Section ◽  
The Mean ◽  
Kolmogorov Criterion ◽  
Mean Square Errors

In practice, photogrammetrists use a single statistic reliability interval criterion, based on the mean square errors, to judge the accuracy of adjustment of photogrammetric blocks. Even in some cases, if the practical and theoretical distributions of frequency interval agree, such a test does not make it possible to establish the closeness of their convergence nor the degree of their difference. In other words, to get a complete picture of the character of the distribution of errors in the adjusted photogrammetric blocks, it is insufficient to investigate any single statistic. In the Research and Development Section of the Topographical Survey Directorate, a computer program (SABA) has been designed to analyze the errors of photogrammetric block adjustments, compute various statistical parameters and check the sample distribution using Kolmogorov criterion. Based on the decision taken, the correspondence between the empirical and theoretical distribution series are checked using the criterion χ2. The program divides the adjusted block to make a comparative evaluation of accuracies in the different sub-blocks. In this case, in addition to Kolmogorov and χ2 tests, the program checks the reliability intervals of the means and mean square errors of the samples and uses Fisher criterion ‘F’ to check the hypothesis of the equality of dispersion. SABA is coded in Fortran IV and Compass for the CDC CYBER 74 and requires a central memory of 28K decimal works. SABA is the acronym for Statistical Analysis of Block Adjustment.

scholarly journals Reversible Markov processes on general spaces and spatial migration processes

2005 ◽  
Vol 37 (3) ◽  
pp. 801-818
Author(s):  
Richard F. Serfozo
Keyword(s):  
Jump Processes ◽  
Markov Jump ◽  
Time Reversibility ◽  
Equilibrium Behavior ◽  
Fundamental Properties ◽  
Markov Jump Processes ◽  
Population Migrations ◽  
Measure Spaces ◽  
Kolmogorov Criterion

In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.

The laws of distribution of some parameters when organizing the movement of trains

2021 ◽  
pp. 27-39
Author(s):  
M. V. Fufacheva ◽  
Keyword(s):  
Coefficient Of Variation ◽  
Least Squares Method ◽  
Erlang Distribution ◽  
Key Factors ◽  
Distribution Law ◽  
Statistical Parameters ◽  
Railway Stations ◽  
Coefficients Of Variation ◽  
Kolmogorov Criterion ◽  
Laws Of Distribution

The article discusses the key factors for the organization of train traffic. The analysis of statistical parameters of the intervals of departure of freight trains from railway stations and the length of the freight train flow is carried out. Based on these train schedules, graphical dependences of the intervals of departure of trains from separate points on the volume of train traffic and the distribution of train lengths in even and odd directions are constructed. Polynomial dependencies with coefficients of variation are derived. The curve of the second-order Erlang distribution function for the departure intervals is constructed. It is determined that the average departure intensity in one hour is equal to three trains, and the average departure interval lies between the 25th and 35th minutes with a probability of 0.793. There is a correlation between the coefficient of variation (mean square deviation) of the departure interval and its average daily deviation. The power function of the analytical ratio of the coefficient of variation from the average interval of departure of freight trains from the technical stations of the Krasnoyarsk railway during the day is determined using the least squares method. The degrees of correspondence of theoretical and statistical distributions of the number of cars in trains are studied using the Kolmogorov criterion with the calculation of the probability value and confirmation that the distribution of the number of cars in trains obeys the binomial law. Using the Pearson agreement criterion, it is proved that the frequency of departure of freight trains from railway stations obeys the exponential distribution law.

On asymptotics of a class of 1-dimensional diffusions

1993 ◽  
Vol 114 (3) ◽  
pp. 499-506
Author(s):  
B. Rajeev
Keyword(s):  
Brownian Motion ◽  
Higher Dimensions ◽  
Fine Tuning ◽  
Law Of Iterated Logarithm ◽  
General Criterion ◽  
Critical Rate ◽  
Related Integral ◽  
Necessary And Sufficient Criteria ◽  
Kolmogorov Criterion ◽  
Necessary And Sufficient

In this paper we study the almost sure asymptotics of htXt where (Xt) satisfies a stochastic differential equation and ht is a deterministic differentiable function, ht ↓ 0 as t → ∞. We give necessary and sufficient criteria, in terms of deterministic integrals, for the process htXt to converge to zero, to oscillate boundedly and for the case of infinite oscillations. Necessary and sufficient criteria for convergence to zero, in terms of a related integral, was studied by Chan and Williams in [1], for a class of diffusions that arise in simulated annealing. In Chan [2] the results are extended to higher dimensions. For Brownian motion, Jeulin and Yor[3] give a general criterion for convergence to zero, when the function ht is merely continuous and non-negative. The results of [1] and [3] are both generalizations of the well known ‘Kolmogorov criterion’ for Brownian motion. Our approach is very close to the techniques developed by Chan and Williams in [1]. Indeed, our method is essentially a fine tuning of those techniques. We apply our results, in Section 3, to a class of diffusions and compute the critical rate ht for which bounded oscillations occur. For Brownian motion this is the law of iterated logarithm, modulo the size of the oscillation. We also consider two parametrized families of diffusions for which the critical rate is seen to depend smoothly on the parameter. These results appear to be new. Our method also gives estimates on the size of the oscillations (Section 6).

scholarly journals Verification of the gauss’s law with the unknown parameters by the Kolmogorov criterion in the problems of railways electric supply

2021 ◽  
Vol 2131 (2) ◽  
pp. 022093
Author(s):  
T M Lindenbaum ◽  
O V Ignatieva
Keyword(s):  
Statistical Modeling ◽  
Contact Line ◽  
Sufficient Accuracy ◽  
Distribution Law ◽  
Unknown Parameters ◽  
Kolmogorov Criterion ◽  
Electric Supply

Abstract Traction currents and voltages in the overhead railroad contact line hypothetically obey the Gauss’s distribution law. An algorithm for statistical modeling of the Kolmogorov distribution for the unknown values of the Gaussian law parameters has been developed. For a large number of the modeling program implementations, it has been shown that testing the hypothesis about the distribution law without taking into account the number of unknown parameters leads to an unacceptable increase in the criterion significance and a decrease in its power. The distribution of the Kolmogorov criterion is calculated with sufficient accuracy for two unknown parameters, which allows its wide practical use.

scholarly journals Analysis of Nonparametric and Parametric Criteria for Statistical Hypotheses Testing. Chapter 1. Agreement Criteria of Pearson and Kolmogorov

2018 ◽  
Vol 83 (4) ◽  
pp. 14-24
Author(s):  
F. V. Motsnyi
Keyword(s):  
Experimental Data ◽  
General Population ◽  
Null Hypothesis ◽  
Mathematical Statistics ◽  
Hypotheses Testing ◽  
Pearson Criterion ◽  
Statistical Hypotheses ◽  
Distribution Laws ◽  
Kolmogorov Criterion ◽  
Statistical Hypotheses Testing

In the statistical analysis of experimental results it is extremely important to know the distribution laws of the general population. ‎Because of all assumptions about the distribution laws are statistical hypotheses, they should be tested. ‎Testing hypotheses are carried out by using the statistical criteria that divided the multitude in two subsets: null and alternative. The ‎null hypothesis is accepted in subset null and is rejected in alternative subset. Knowledge of the distribution law is a prerequisite for the use of numerical mathematical methods. The hypothesis is accepted if the divergence between empirical and theoretical distributions will be random. The hypothesis is rejected if the divergence between empirical and theoretical distributions will be essential. There is a number of different agreement criteria for the statistical hypotheses testing. The paper continues ideas of the author’s works, devoted to advanced based tools of the mathematical statistics. This part of the paper is devoted to nonparametric agreement criteria. Nonparametric tests don’t allow us to include in calculations the parameters of the probability distribution and to operate with frequency only, as well as to assume directly that the experimental data have a specific distribution. Nonparametric criteria are widely used in analysis of the empirical data, in the testing of the simple and complex statistical hypotheses etc. They include the well known criteria of K. Pearson, A. Kolmogorov, N. H. Kuiper, G. S. Watson, T. W. Anderson, D. A. Darling, J. Zhang, Mann – Whitney U-test, Wilcoxon signed-rank test and so on. Pearson and Kolmogorov criteria are most frequently used in mathematical statistics. Pearson criterion (-criterion) is the universal statistical nonparametric criterion which has -distribution. It is used for the testing of the null hypothesis about subordination of the distribution of sample empirical to theory of general population at large amounts of sample (n>50). Pearson criterion is connected with calculation of theoretical frequency. Kolmogorov criterion is used for comparing empirical and theoretical distributions and permits to find the point in which the difference between these distributions is maximum and statistically reliable. Kolmogorov criterion is used at large amounts of sample too. It should be noted, that the results obtained by using Pearson criterion are more precise because practically all experimental data are used. The peculiarities of Pearson and Kolmogorov criteria are found out. The formulas for calculations are given and the typical tasks are suggested and solved. The typical tasks are suggested and solved that help us to understand more deeply the essence of Pearson and Kolmogorov criteria.

Determination of Boundary Parameters of Pipelines Elbows Blanking Elements Made from Titanium Alloy Ti-4Al-2Mn and Steel AISI 304

2019 ◽  
Vol 822 ◽  
pp. 178-184
Author(s):  
Konstantin Nokolenko ◽  
Kirill Nikolenko ◽  
Sergey Zvonov ◽  
Alina Lopatina
Keyword(s):  
Computer Simulation ◽  
Titanium Alloy ◽  
Bend Angle ◽  
Aisi 304 ◽  
Degree Of Deformation ◽  
Plastic Materials ◽  
Steel Aisi ◽  
Kolmogorov Criterion

The results of computer simulation processing and determination of limiting degree of deformation by the Kolmogorov criterion are presented. The derivation of the dependence for the evaluation of the destruction of low-plastic materials at the edge is made at bend angle of 900

scholarly journals Reversible Markov processes on general spaces and spatial migration processes

2005 ◽  
Vol 37 (03) ◽  
pp. 801-818
Author(s):  
Richard F. Serfozo
Keyword(s):  
Jump Processes ◽  
Markov Jump ◽  
Time Reversibility ◽  
Equilibrium Behavior ◽  
Fundamental Properties ◽  
Markov Jump Processes ◽  
Population Migrations ◽  
Measure Spaces ◽  
Kolmogorov Criterion

In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.

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