Distribution Density Function P(S) of Self-Avoiding Walk Chains

Mathematical model of unidirectional fibrous polymer composite material with optical fiber sensor built into reinforcing fiber (filament of elementary fibers) with distributed Bragg grating is developed in order to diagnoste defects of filament impregnation - finding probability of impregnation defect as relative length of local sections of filament without impregnation, i.e. without filling binder of space between its elementary fibers. The technique of digital processing of reflection spectrum according to the solution of the integral Fredholm equation of the 1st kind is used in order to find the desired informative function of density of distribution of axial strains along the length of the sensitive section of the fibre-optic sensor. The approach assumes that the optical fiber sensor is embedded in the composite material at the stage of its manufacture, wherein the low-reflective nature of the sensitive portion of the optical fiber allows linear summation of reflection coefficients from its various local portions regardless of their mutual positions. Algorithm of numerical processing of strain distribution density function is developed for finding of sought probability of presence of impregnation defects along filament length. It has been revealed that the distribution density function has pronounced informative pulses, from the location and value of which the sought-after values of probability of presence of impregnation defects along the length of the filament can be found. The results of diagnostics of different values of the sought probability of the filament impregnation defect are presented based on the results of numerical simulation of the measured reflection spectra and the sought function of strain distribution density along the length of the sensitive section of the optical fiber sensor at different values of the volume fraction of the filaments, combinations of transverse and longitudinal loads of the representative domain of the unidirectional fibrous composite material in comparison with graphs for the case without load.

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Verification of recovery of distribution density function of the random variable by methods of nonparametric statistics

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/481/1/012004 ◽

2019 ◽

Vol 481 ◽

pp. 012004 ◽

Cited By ~ 2

Author(s):

V N Syzrantsev ◽

K V Syzrantseva

Keyword(s):

Density Function ◽

Distribution Density ◽

Random Variable ◽

Nonparametric Statistics ◽

Distribution Density Function

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Polynomials, numerical triangles and sequences associated with the probability distribution of the hyperbolic cosine type for odd values of the parameter

Journal of Physics Conference Series ◽

10.1088/1742-6596/2052/1/012045 ◽

2021 ◽

Vol 2052 (1) ◽

pp. 012045

Author(s):

M S Tokmachev

Keyword(s):

Probability Distribution ◽

Density Function ◽

Distribution Density ◽

Stirling Numbers ◽

Practical Significance ◽

New Class ◽

Distribution Density Function ◽

Physical Problems ◽

Hyperbolic Cosine ◽

And Algebra

Abstract The article introduces a new class of polynomials that first appeared in the probability distribution density function of the hyperbolic cosine type. With an integer change in one of the parameters of this distribution, polynomials in the form of a product of positive factors are written out with an increasing degree. Earlier, the author found a connection between the distribution of the hyperbolic cosine type and numerical sets, in particular, in the simplest cases with the triangle of coefficients of Bessel polynomials, the triangle of Stirling numbers, sequences of coefficients in the expansion of various functions, etc. Also from the distribution formed numerous numerical sequences, both new and widely known. Consideration of polynomials separately from the density function made it possible to reconstruct numerical sets of coefficients, ordered in the form of numerical triangles and numerical sequences. The connections between the elements of the sets are established. Among the sequences obtained, in the simplest cases, there are those known from others, for example, physical problems. However, the overwhelming majority of the found number sets have not been encountered earlier in the literature. The obvious applications of this research are number theory and algebra. And the interdisciplinarity of the results indicates the possibility of applications and enhances their practical significance in other areas of knowledge.

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MODEL REGRESI LINIER BAYESIAN DENGAN APLIKASI PADA DATA PENUNDAAN PENERBANGAN

Journal of Fundamental Mathematics and Applications (JFMA) ◽

10.14710/jfma.v1i2.21 ◽

2018 ◽

Vol 1 (2) ◽

pp. 74

Author(s):

Vemmie Nastiti Lestari ◽

Subanar Subanar

Keyword(s):

Linear Regression ◽

Density Function ◽

Linear Regression Model ◽

Distribution Density ◽

Large Datasets ◽

Simulation Data ◽

Distribution Density Function ◽

Bayesian Linear Regression ◽

Flight Delay ◽

Statistical Summary

Bayesian linear regression is an approach to linear regression where statistical analysis depend of Bayesian inference. The Bayesian model on big data uses a summary of data statistics as input; Statistical summary can be calculated from each subset, then a statistical summary of the full dataset is obtained from the sum of the summary statistics for each subset. Recent developments in data science and research, produce large datasets that are too large to be analyzed as a whole due to the limitations of computer memory or storage capacity. To overcome this, a program package was introduced from R namely BayesSummaryStatLM for the Bayesian linear regression model with the Markov Chain Monte Carlo implementation that overcomes this limitation. Then the program package from R, ff is used to read data in large datasets while calculating statistics summary. In this study Bayesian linear regression model used with several choices of prior distribution for unknown model parameters, and illustrates in simulation data and real datasets for flight delay data in US 2008. The application of simulation data and flight delay data produces a plot of density functions for the β parameters has a shape resembling a plot of Normal distribution density function, whereas for plot parameters the density function has a shape resembling the plot of Inverse Gamma distribution density function. In the simulation data, the estimator for each parameter produced has a value that approach to the value of the specified parameter (True Value). This is also indicated by the narrow credible interval for each parameters.

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The discounted local limit theorems for large deviations

Lietuvos matematikos rinkinys ◽

10.15388/lmr.2008.18152 ◽

2008 ◽

Vol 48 ◽

Author(s):

Leonas Saulis ◽

Dovilė Deltuvienė

Keyword(s):

Large Deviations ◽

Density Function ◽

Limit Theorems ◽

Distribution Density ◽

Normal Approximation ◽

Random Variables ◽

Local Limit ◽

Distribution Density Function ◽

Local Limit Theorems

Theorems of large deviations, both in the Cramer zone and the Linnik power zones, for the normal approximation of the distribution density function of normalized sum Sv = \sum∞ k=0 vkXk, 0 < v < 1, of i.i.d. random variables (r.v.) X0, X1, . . . satisfying the generalized Bernstein’s condition are obtained.

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