scholarly journals Mathematical modeling on the base of functions density of normal distribution

2021 ◽  
Vol 12 (33) ◽  
pp. 34-49
Author(s):  
Iuliia Pinkovetskaia ◽  
Yulia Nuretdinova ◽  
Ildar Nuretdinov ◽  
Natalia Lipatova
Keyword(s):  
Normal Distribution ◽  
Empirical Data ◽  
Comprehensive Evaluation ◽  
Statistical Tests ◽  
Methodological Approach ◽  
Distribution Functions ◽  
Density Functions ◽  
Large Sets ◽  
Kolmogorov Smirnov

One of the urgent tasks in many modern scientific studies is the comparative analysis of indicators that characterize large sets of similar objects located in different regions. Given the significant differences between the regions compared, this analysis should be carried out using relative indicators. The objective of the study was to use the density functions of the normal distribution to model empirical data that describe the compared sets of objects located in different regions. The methodological approach was based on the Chebyshev and Lyapunov theorems. The research results focus on the main stages of the construction of normal distribution functions and the corresponding histograms, as well as the determination of the parameters of these functions. The work possesses a degree of originality, since it provides answers to questions such as the justification of the necessary information base; performing computational experiments and developing alternative options for the generation of normal distribution density functions; comprehensive evaluation of the quality of the functions obtained through three statistical tests: Pearson, Kolmogorov-Smirnov, Shapiro-Wilk; identification of patterns that characterize the distribution of indicators of the sets of objects considered. Examples of empirical data models are given using distribution functions to estimate the share of innovative firms in the total number of firms in the regions of Russia.

scholarly journals Dynamical Age Determination of Open Clusters

1980 ◽  
Vol 85 ◽  
pp. 221-222
Author(s):  
M. Buchholz ◽  
Th. Schmidt-Kaler
Keyword(s):  
Age Determination ◽  
Dynamical Theory ◽  
Distribution Functions ◽  
Open Clusters ◽  
Kolmogorov Smirnov ◽  
The Difference ◽  
Absolute Age ◽  
Image Position ◽  
Smirnov Test

The radial mass distribution (obtained by counting stars in strips) of the real cluster is compared successively to the distribution functions of a simulated cluster of 100 stars, each of which corresponds to a certain dynamical age, Tdyn, The value of Tdyn, belonging to the function most similar to the observed one is taken to be the dynamical age of the cluster. The radius is given in units of R1/2 (sphere containing half of the total mass); this unit is nearly time-independent. The difference between the distribution functions is measured by the maximum Δmax of the Kolmogorov-Smirnov test which is free from assumptions on the form of the distributions. The minimum in the plot Δmax vs Tdyn, indicates the age of the cluster. It is then converted into an absolute age, Tabs (in years), by The error due to the dynamical theory (limited number of distribution functions, etc.) is estimated at 12%, the error due to the uncertainty of diameter and mass of the cluster is about 30%. Unreliable results were obtained in case of strongly inhomogeneous reddening of the cluster. As an example, the plot of the test values for NGC 457 is given in Figure 1.

scholarly journals The age structure of the scientific and pedagogical staff: data from the regions of Russia

2021 ◽  
Vol 14 (33) ◽  
pp. e16491
Author(s):  
Iuliia S. Pinkovetskaia
Keyword(s):  
Higher Education ◽  
Normal Distribution ◽  
Age Structure ◽  
Methodological Approach ◽  
Age Groups ◽  
Statistical Information ◽  
Educational Institutions ◽  
Density Functions ◽  
Regional Features ◽  
Regions Of Russia

The purpose of our study was to evaluate the indicators characterizing the age structure of the scientific and pedagogical staff of universities and other higher educational institutions in the regions of Russia. In the course of the work, the indicators characterizing the specific weights of teachers belonging to five age groups from 25 to 34 years, from 35 to 44 years, from 45 to 54 years, from 55 to 64 years and over 65 years in the total number of teachers working in higher education institutes were evaluated. The study used official statistical information for 82 regions of Russia. We used the density functions of the normal distribution as models. The results of the research allowed us to draw conclusions: the largest number (more than a quarter) of teachers was observed in the group from 35 to 44 years; 24% of teachers were aged from 45 to 54 years; 20% of teachers were slightly older. The least number of teachers was observed in the age groups over 65 years and from 25 to 34 years. The proposed methodological approach and the results obtained have originality and scientific novelty, since the assessment of regional features of the age structure of scientific and pedagogical personnel in the regions of Russia has not been carried out before.

scholarly journals Gender differences in solo entrepreneurship in modern countries

2021 ◽  
Vol 12 (34) ◽  
pp. 224-238
Author(s):  
Iuliia Pinkovetskaia ◽  
Natalia Neif ◽  
Aleksandra Navasardyan ◽  
Tatyana Treskova ◽  
Marina Yashina
Keyword(s):  
Mathematical Modeling ◽  
Gender Differences ◽  
Normal Distribution ◽  
Gender Gap ◽  
Empirical Data ◽  
Density Functions ◽  
Initial Information ◽  
Global Entrepreneurship ◽  
The Creation ◽  
National Economies

Aim of the study is to evaluate the indicators describing the level of solo entrepreneurship among women and men who are beginning entrepreneurs in different countries. Empirical data provided in the Global Entrepreneurship Monitoring Project for fifty-nine countries were used as initial information in calculations. Economic and mathematical modeling was based on development of density functions normal distribution. In the study, three indicators describing solo entrepreneurship in 59 countries were evaluated: share of solo entrepreneurs-women in the total number of women who participate in the creation of their own businesses in different countries; share of solo entrepreneurs-men in total number of men who participate in creation of their own businesses in different countries; ratio of the above-mentioned shares of solo entrepreneurs of women and men. Average values and ranges of changes in considered indicators were determined, which are typical for most countries. In addition, national economies that are characterized by high and low values of each of the three indicators were identified. The study showed that there is a gender gap in the values of indicators in most countries. It is proved that share of women involved in solo entrepreneurship in most countries is higher than that of men.

scholarly journals Stochastic Properties of Confidence Ellipsoids after Least Squares Adjustment, Derived from GUM Analysis and Monte Carlo Simulations

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1318 ◽  
Author(s):  
Wolfgang Niemeier ◽  
Dieter Tengen
Keyword(s):  
Monte Carlo ◽  
Normal Distribution ◽  
Statistical Tests ◽  
Point Clouds ◽  
Satellite System ◽  
Uncertainty Assessment ◽  
Distribution Functions ◽  
Station Coordinates ◽  
Stochastic Properties ◽  
Confidence Ellipsoids

In this paper stochastic properties are discussed for the final results of the application of an innovative approach for uncertainty assessment for network computations, which can be characterized as two-step approach: As the first step, raw measuring data and all possible influencing factors were analyzed, applying uncertainty modeling in accordance with GUM (Guide to the Expression of Uncertainty in Measurement). As the second step, Monte Carlo (MC) simulations were set up for the complete processing chain, i.e., for simulating all input data and performing adjustment computations. The input datasets were generated by pseudo random numbers and pre-set probability distribution functions were considered for all these variables. The main extensions here are related to an analysis of the stochastic properties of the final results, which are point clouds for station coordinates. According to Cramer’s central limit theorem and Hagen’s elementary error theory, there are some justifications for why these coordinate variations follow a normal distribution. The applied statistical tests on the normal distribution confirmed this assumption. This result allows us to derive confidence ellipsoids out of these point clouds and to continue with our quality assessment and more detailed analysis of the results, similar to the procedures well-known in classical network theory. This approach and the check on normal distribution is applied to the local tie network of Metsähovi, Finland, where terrestrial geodetic observations are combined with Global Navigation Satellite System (GNSS) data.

scholarly journals Motivation of new entrepreneurs in modern economies

2020 ◽  
Vol 9 (29) ◽  
pp. 368-373
Author(s):  
I.S. Pinkovetskaia ◽  
Diego Felipe Arbeláez-Campillo ◽  
Magda Julissa Rojas-Bahamón ◽  
Daniela S. Veas Iniesta
Keyword(s):  
Initial Data ◽  
Mathematical Models ◽  
Normal Distribution ◽  
Empirical Data ◽  
Distribution Functions ◽  
Global Entrepreneurship ◽  
National Economies ◽  
Monitoring Report

Recent decades have shown an increasing role of entrepreneurship in both economically developed and developing national economies. The purpose of the research is the estimation of the indicators that describe the proportion of voluntary, demanding and forced entrepreneurs in the total number of early entrepreneurs. The existing ratio of entrepreneurs with different motivation was also evaluated. The study used empirical data obtained in 2018 and presented in the Global entrepreneurship monitoring report. The normal distribution functions were used to develop economic and mathematical models for approximating initial data and evaluating four indicators of early entrepreneurs motivation in different countries.

Tire Treadwear — A Comprehensive Evaluation of the Factors: Generic Type, Aspect Ratio, Tread Pattern, and Tread Composition Part I: Introduction and Details on the Organization of the Program

1986 ◽  
Vol 14 (4) ◽  
pp. 201-218 ◽  
Author(s):  
A. G. Veith
Keyword(s):  
Aspect Ratio ◽  
Comprehensive Evaluation ◽  
Test Method ◽  
Interactive Effects ◽  
Data Analyses ◽  
Main Effect ◽  
Systematic Determination ◽  
Relationship Of ◽  
The Relationship

Abstract This four-part series of papers addresses the problem of systematic determination of the influence of several tire factors on tire treadwear. Both the main effect of each factor and some of their interactive effects are included. The program was also structured to evaluate the influence of some external-to-tire conditions on the relationship of tire factors to treadwear. Part I describes the experimental design used to evaluate the effects on treadwear of generic tire type, aspect ratio, tread pattern (groove or void level), type of pattern (straight rib or block), and tread compound. Construction procedures and precautions used to obtain a valid and functional test method are included. Two guiding principles to be used in the data analyses of Parts II and III are discussed. These are the fractional groove and void concept, to characterize tread pattern geometry, and a demonstration of the equivalence of wear rate for identical compounds on whole tread or multi-section tread tires.

Determination of Specific Activity of Cholera Chemical Vaccine Components using Cell Culture

2020 ◽  
Vol 36 (3) ◽  
pp. 82-89
Author(s):  
O.V. Gromova ◽  
O.S. Durakova ◽  
S.V. Generalov ◽  
L.F. Livanova ◽  
O.A. Volokh
Keyword(s):  
Cell Culture ◽  
Vibrio Cholerae ◽  
Production Control ◽  
Specific Activity ◽  
Methodological Approach ◽  
Toxin Production ◽  
Submerged Cultivation ◽  
Vaccine Production ◽  
Antigenic Activity

Том 36(2020) №3 стр. 82-89; DOI 10.21519/0234-2758-2020-36-3-82-89А.В. Гаева1*, О.В. Громова1, О.С. Дуракова1, С.В. Генералов1, Л.Ф. Ливанова1, О.А. Волох1 Определение специфической активности компонентов холерной химической вакцины с использованием культуры клеток 1ФКУЗ «Российский научно-исследовательский противочумный институт «Микроб»» Федеральной службы по надзору в сфере защиты прав потребителей и благополучия человека, Саратов 410005 *[email protected] Поступила - 2019-11-26; После доработки - 2020-03-16; Принята к публикации - 2020-05-15 Список литературы Описаны методы определения динамики продукции токсинов штаммом Vibrio cholerae 569B при глубинном культивировании в биореакторе и антигенной активности специфической фракции холерогена-анатоксина по анатоксинсвязыванию с использованием клеточных культур. Показана высокая степень соответствия результатов, полученных методами, применяемыми для контроля этапов производства холерной химической вакцины и рассмотренными в данной работе. Отмечено, что применение клеточной линии СНО-К1 наиболее перспективно для замены биомоделей на промежуточных этапах контроля активных компонентов холерной химической вакцины. Разработанный методический подход впервые предлагается использовать на этапах производства холерной бивалентной химической вакцины. культура клеток, Vibrio cholerae, холерная химическая вакцина, контроль производства, холера. Vol 36(2020) N 3 p. 82-89; DOI 10.21519/0234-2758-2020-36-3-82-89A.V. Gaeva1*, O.V. Gromova1, O.S. Durakova1, S.V. Generalov1, L.F. Livanova1, O.A. Volokh1 Determination of Specific Activity of Cholera Chemical Vaccine Components using Cell Culture 1Russian Research Anti-Plague Institute «Microbe» of the Federal Service for Surveillance on Consumer Rights Protection and Human Wellbeing, Saratov, 410005 *[email protected] Received - 26.11.2019; Accepted - 15.05.2020 References The methods has been described to determine the dynamics of toxin production by the Vibrio cholerae 569B strain during submerged cultivation in bioreactor and of the antigenic activity of specific choleragen anatoxin fraction by anatoxin binding levels using cell cultures. High degree of consistency was observed between the results obtained via the method under consideration and those obtained via control methods at different stages of cholera chemical vaccine production. It was shown that the CHO-K1 cell line is the most promising substitute for biomodels at the intermediate stages of control of active cholera chemical vaccine components. The developed methodological approach was first proposed for use at the stages of cholera chemical bivalent vaccine manufacturing. cell culture, Vibrio cholerae, cholera chemical vaccine, production control, cholera.

scholarly journals Managing pH of Organic Matrices and New Commercial Substrates for Ornamental Plant Production: A Methodological Approach

Agronomy ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 851
Author(s):  
Sonia Cacini ◽  
Sara Di Lonardo ◽  
Simone Orsenigo ◽  
Daniele Massa
Keyword(s):  
Methodological Approach ◽  
Buffering Capacity ◽  
Ornamental Plant ◽  
Plant Production ◽  
Climatic Chamber ◽  
Step Procedure ◽  
Coir Dust ◽  
Organic Matrices ◽  
Substrate Mixtures

Professional peat-free substrates for ornamental plant production are increasingly required by nursery growers. Most promising materials are green compost, coconut coir dust, and woody fibre, used alone or in mixtures. One of the major concerns is pH, usually higher than optimal. In this work, a method based on a three-step procedure was adopted to acidify three organic matrices alone or in mixtures and to individuate the most suitable product, between iron(II) sulphate 7-hydrate and elemental sulphur chips. Firstly, the determination of the buffering capacity by dilution with sulphuric acid was carried out to determine dosages. Afterwards, an incubation trial of 84 (iron(II) sulphate) or 120 days (sulphur chips) was conducted on matrices and substrate mixtures with calculated doses in a climatic chamber maintained at 21 °C. Iron(II) sulphate resulted not suitable because it caused a rapid, but not lasting, pH lowering and an excessive electrical conductivity (EC) increase. Sulphur chips could instead guarantee an adequate and lasting pH lowering. These results were then validated in the open field trial on matrices and substrates. The proposed acidification methodology could be considered in developing new substrates, but the rapidity of pH acidification and EC increase on plant and mineral nutrition should be further investigated.

scholarly journals Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions—Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 31
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Position Error ◽  
Positioning System ◽  
Navigation Systems ◽  
Mean Square ◽  
Positioning Systems ◽  
Position Errors ◽  
System Errors

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.

scholarly journals Particle Size Distribution of Various Soil Materials Measured by Laser Diffraction—The Problem of Reproducibility

Minerals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 465
Author(s):  
Cezary Polakowski ◽  
Magdalena Ryżak ◽  
Agata Sochan ◽  
Michał Beczek ◽  
Rafał Mazur ◽  
...  
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Normal Distribution ◽  
Size Distribution ◽  
Precise Measurement ◽  
Soil Analysis ◽  
Statistical Tests ◽  
Diffraction Method ◽  
Laser Diffraction ◽  
Method Analysis

Particle size distribution is an important soil parameter—therefore precise measurement of this characteristic is essential. The application of the widely used laser diffraction method for soil analysis continues to be a subject of debate. The precision of this method, proven on homogeneous samples, has been implicitly extended to soil analyses, but this has not been sufficiently well confirmed in the literature thus far. The aim of this study is to supplement the information available on the precision of the method in terms of reproducibility of soil measurement and whether the reproducibility of soil measurement is characterized by a normal distribution. To estimate the reproducibility of the laser diffraction method, thirteen various soil samples were characterized, and results were analysed statistically. The coefficient of variation acquired was lowest (3.44%) for silt and highest for sand (23.28%). Five of the thirteen tested samples were characterized by a normal distribution. The fraction content of eight samples was not characterized by normal distribution, but the extent of this phenomenon varied between soils. Although the laser diffraction method is repeatable, the measurement of soil particle size distribution can have limited reproducibility. The main cause seems to be small amounts of sand particles. The error can be amplified by the construction of the dispersion unit. Non-parametric statistical tests should be used by default for soil laser diffraction method analysis.

Sign in / Sign up

Export Citation Format

Share Document