Terms Of Gaussian Distribution Research Articles

구조방정식모형에서 경로계수에 대한 검정 방법들의 제2종 오류 평가

When performing data analysis using a structural equation model, the main concern is the estimation and testing of path coefficients. Testing methods for path coefficients include the t-value method, Satorra-Bentler's scaling testing statistic method, and Bollen-Stine's bootstrap method. All of these methods are asymptotic testing methods that assume a normal distribution of data, and may provide different testing results depending on the type of given data and model. In this study, the testing power (1-type 2 errors) was calculated under various circumstances using simulations for the testing methods that are mainly used, and the performance of these testing methods was evaluated through the results. The ML method was found to have robust properties in deviation from normal distribution in terms of estimation and power. Also, in most situations, the power of the Satorra-Bentler scaling testing was greater than that of the ML method. And in some situations, when the sample size is small, the power of the bootstrap method based on WLS was slightly smaller than that of other methods. Although the results of this study cannot be generalized in all situations, it is thought that they can be referenced in various fields of research using structural equation models.

Ön Lisans Öğrencilerinin Bilgi Güvenliği Kazanımı Ve Farkındalık Düzeylerinin Belirlenmesi: Kırıkhan Meslek Yüksekokulu Örneği

Bu çalışmanın amacı, önlisans öğrencilerinin bilgi güvenliği konusundaki kazanım ve farkındalık düzeylerinin belirlenmesidir. Çalışma tarama modelinde tasarlanmıştır. Örneklem seçiminde kolayda örnekleme yöntemi kullanılmıştır. Bu bağlamda, araştırmanın örneklemini Kırıkhan Meslek Yüksekokulu’nda çeşitli bölümlerde öğrenim gören 161 önlisans öğrencisi oluşturmaktadır. Çalışmada Bilgi Güvenliği Kazanımları (BGK) ve Bilgi Güvenliği Farkındalığı (BGF) ölçekleri kullanılmıştır. Demografik bilgiler için betimsel istatistikler kullanılırken, araştırmaya katılanların yaş ve bölüm değişkenleri için tek yönlü ANOVA testi, sınıf düzeyi için bağımsız örneklem t-testi uygulanmıştır. Bu çalışmanın sonucunda, önlisans öğrencilerinin bilgi güvenliği farkındalık düzeylerinin yüksek, bilgi güvenliği kazanım düzeylerinin orta düzeyde olduğu belirlenmiştir. Öğrencilerin BGK ortalama puanlarının öğrenim gördükleri programlara göre istatistiksel olarak önemli ölçüde farklılık gösterdiği tespit edilmiştir. Aynı zamanda öğrencilerin BGF alt boyutlarından olan İnternet Tarayıcısı ve Ağ Güvenliği puanlarının öğrencilerin yaşlarına göre önemli ölçüde farklılık gösterdiği bulunmuştur. Bununla birlikte önlisans öğrencilerinin bilgi güvenliği kazanımları ve alt boyutları ile bilgi güvenliği farkındalığı internet güvenliği, internet tarayıcısı ve ağ güvenliği alt boyutlarına göre bilgi güvenliğine ilişkin bilişim suçlarını bilme durumuna göre de önemli ölçüde farklılık gösterdiği bulunmuştur. Öğrencilerin bilgi güvenliği farkındalığı (BGF) ortalama puanları ile bilgi güvenliği kazanımları (BGK) ve tüm BGK alt boyutlarına ait ortalama puanlarının öğrencilerin sınıf düzeylerine göre istatistiksel olarak önemli ölçüde bir farklılık göstermediği tespit edilmiştir.

Evaluation of the Gauss Integral

The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler–Poisson) integral over a finite boundary, as is necessary, for instance, for the error function or the cumulative distribution of the normal distribution, cannot be expressed by analytic functions. This is proven by the Risch algorithm. Regardless, there are proposals for approximate solutions. In this paper, we give a new solution in terms of normal distributions by applying a geometric procedure iteratively to the problem.

The Relationship Between the Reputation of the Sports Team Perceived by University Students and Their Psychological Commitments to Their Teams

This study aims to examine the relationship between the reputation of sports team perceived by university students and their psychological commitment to their teams and to determine whether these two variables differ according to variables such as gender, age, department of university, the status of membership to a fan union, and the team the students supported. This is a quantitative study utilizing descriptive scanning model. The population of the study consists of students studying in universities on the European Side of Istanbul, and the sample consists of 219 students contacted by the random selection method. The study applied personal information form prepared by the researcher, the Spectator-Based Sports Team Reputation Scale (SSTR), which was developed by Wonseok et al. (2015) and the Fan Psychological Commitment Scale (FPCS), which was developed by Matsuoka (2001) in order to collect data in the study. SPSS 20.0 software package was used for data analysis. The collected data were examined with Kolmogorov-Smirnov and distribution graphs in terms of normal distribution in addition to descriptive statistics. Mann-Whitney U and Kruskal-Wallis tests were used to compare the data based on the number of variables. Post-hoc analyses were conducted by Mann-Whitney U test using Bonferroni correction and relationships between variables by Spearman’s correlation analysis. The prediction of the FPCS score by SSTR score was evaluated through linear regression analysis. The error margin was accepted as p < 0.05. A positive significant relationship was found between FPCS and SSTR variables perceived by university students according to the research results (p < 0.05). The results have strategic implications for managers who can evaluate the team reputation and the psychological commitment of the fan to the team in this context and encourage this for more fan participation.

INVESTIGATION OF THE RELATIONSHIP BETWEEN THE RESPONSES TO CANCER AND RELIGIOUS COPING STYLES OF NEWLY DIAGNOSED BREAST CANCER PATIENTS

This research is a descriptive study conducted to assess the relationship between the responses to cancer by patients newly diagnosed with breast cancer and their religious coping.The study included 150 newly diagnosed breast cancer patients who received chemotherapy from November 2016/ April 2017 in the outpatient chemotherapy unit of a private university hospital. As a data collection tool, the questionnaire containing the descriptive and demographic characteristics of the patients, the scale of response style to cancer, and the religious coping style scale were used in the study. The data of the research were analyzed in terms of normal distribution by using the Shapiro-Wilks normality test. Since the data did not show normal distribution, the Mann-Whitney U test was used in two independent group comparisons, and the Kruskal-Wallis test was used in comparisons between more than two independent groups.Spearman correlation analysis was used to assess the relationship between scales. The predictive level of the Religious Coping Subscales to the Cancer Response subscale scores was evaluated by linear regression analysis. In the study, spiritual struggling subscale score within the scale of response to cancer was 51.81+4.95, the helplessness-despair subscale score was 9.85+2.39, anxious anticipate subscale score was 23.54+2.35, the fatalist subscale score was 19.98+1.59, and deny subscale score was 1.73+0.67.In other words, it was determined that the spiritual struggling soul was highly used by patients in response to cancer. In the study, the positive religious coping scale scores were 23.16+3.27, and negative religious coping scores were 7.72+1.77, which mean that most of the patients had positive religious coping scores. A positive correlation was found between the positive religious coping score and the spiritual struggling score (p<0.05; r=0.440). As the positive religious coping increases, the patients' struggle with disease is increasing. It has been observed that there is a relationship between cancer responses and religious coping of newly diagnosed breast cancer patients.

ÖĞRETMENLERİN ALTERNATİF ÖLÇME DEĞERLENDİRME TEKNİKLERİNİ KULLANIMINA YÖNELİK YETERLİK ALGILARININ İNCELENMESİ

The purpose of this research is to reveal teachers' perceptions of competence towards using alternative measurement and evaluation techniques. Participants of the study are teachers working in primary, secondary and high schools in Sivas city center. The data were collected between September and November 2019. In the study, “self-efficacy scale for alternative measurement and evaluation approaches” was used to collect data. Cronbach's Alpha reliability coefficient of the scale was examined and it was concluded that the scale was reliable. The data obtained were examined in terms of normal distribution and the Kolmogorov-Smirnov test showed that the data were distributed normally. Independent groups t-test was used for the participants' gender, educational status and in-service training, and ANOVA test was used for the education level and seniority variables. As a result of the research, it was found that teachers' perceptions of competence towards using alternative measurement and evaluation techniques did not make a significant difference according to gender. It was concluded that there was a significant difference in terms of educational status, in-service training, education level and seniority variables. As a result of the research, it is suggested that teachers should be encouraged to do postgraduate education in order to ensure their personal development and that teachers should be supported by establishing a measurement and evaluation unit in the school.

A stable quantum Darmois-Skitovich theorem

The Darmois-Skitovich theorem is a simple characterization of the normal distribution in terms of the independence of linear forms. We present here a non-commutative version of this theorem in the context of Gaussian bosonic states and show that this theorem is strongly stable under small errors in its underlying conditions. An explicit estimate of the stability constants which depend on the physical parameters of the problem is given.

Satisfaction Levels of Sports Event Participants

The aim of the study is to compare the satisfaction levels of the participants, participating in the sports festival according to some variables. The survey was conducted to 1,274 people randomly selected among approximately 55,000 participants who participated in the sports festival organized by a municipality in Denizli-Turkey. As a data collection tools “Personal Information Form” prepared by the researchers and the “Festival Satisfaction Survey” which was developed by Yoon et al. (2010) and adopted into Turkish by Tayfun and Arslan (2013). The data collection forms applied to the participants during the festival and the data were checked in terms of normal distributions in the statistical analysis program and analyzed by using independent samples T test and ANOVA analysis methods. As a result of the analysis, male participants perceived a significant level of satisfaction in the sub-dimensions of program, value, satisfaction and loyalty from the questionnaire. A significant difference was found in the sub-dimensions of knowledge, value, satisfaction, and loyalty in the examination conducted by occupational groups. It is seen that this difference is caused by the public employees’ higher satisfaction level. Another hypothesis of the study was to compare the satisfaction of participants according to their educational status. Significant differences were found in the sub-dimensions of knowledge, value, satisfaction, loyalty. It is seen that reason for the statistically meaningful difference, primary school graduates feel lower satisfaction from the festival in terms of education level. As a result, it is thought that participants of the sport festivals feel different satisfaction in terms of their gender, education status and working situation and while planning that kind of events these characteristics must be taken into consideration.

Mineral Systems, Their Types, and Distributions in Nature: 3. Otto Mountain (USA) and El Dragon (Bolivia) Deposits

It was found that in minerals, 27 chemical elements are essential species-defining constituents in all tellurium-bearing mineral species known up to 2018 (166). The number of minerals containing these leading elements were calculated as follows (parentheses): O (85), H (47), Cu (42), Pb (39), Bi (30), S (26), Fe (20), Ag (18), Pd (15), Cl (13); Zn Au (11 minerals each); Ca, Se (7 minerals each); Mg, Mn, Sb, As (6 minerals each); Ni, Hg (5 minerals each); U (4), Ir (3); Al, K, C, Sn, Pt (2 minerals each). It has been revealed that the majority of species-defining elements show a normal distribution in terms of mineral systems. A comparative analysis of the mineral species distribution based on various systems was carried out for the Otto Mountain (USA) and El Dragon (Potosi, Bolivia) deposits, as well as comparison of these objects based on the distribution of these species-defining elements. It was found that Cu, Pb, Au, S, C are “abundant” species-defining elements in minerals of both deposits, and Si, Ca, K, Al are deficient, “scarce” elements in both cases. Minerals containing Te, Cr, Cl, Ag, I, As, Mo, P, Sr, V, U, Na, and F are present only in the Otto Mountain mine, and minerals with Mg, Ba, Ni, Hg, and Co were detected only in El Dragon. The amount of O, H, Si, Pb-bearing minerals is substantially higher in Otto Mountain ores than in El Dragon ores.

Uncertainty in electricity markets from a semi-nonparametric approach

This paper introduces a semi-nonparametric (SNP) methodology for the modeling of skewness, leptokurtosis and high-order moments in electricity markets. We highlight the importance of accurately measuring these features in many contexts (e.g. design of power plants with different technologies, fuel prices, and energy demand) and the need for using flexible non-normal densities. We show that the SNP approach describes the uncertainty in an electricity markets, reducing the limitations that normality and parametric density functions impose. Our application covers a wide variety of Colombian electricity variables, including spot price, national energy demand, the climate index ONI, and the series of hydrologic inflows for different rivers. For such variables we find that the SNP outperforms the normal distribution in terms of accuracy measures based on maximum likelihood estimation. As a result, our methodology has direct applications for risk analysis and portfolio choice related to electricity markets and for implementing policies on electricity markets that improve efficiency and sustainability.

APPLICATON OF MICROSEISMIC NOISE ESTIMATION IN OIL AND GAS EXPLORATION AIMED AT REDUCING ENVIRONMENTAL IMPACT

Aim. This article discusses the possibility of reducing ecological costs and risks during exploration of oil and gas fields. To this end, we propose to reduce the number of exploratory drilling works performed using unjustified non‐productive wells. Such a problem can be solved with the help of innovative seismic‐acoustic methods of direct deposit exploration.Methods. The method of microseismic noise estimation (MNE) in application to hidden hydrocarbon de‐ posits is proposed. When implementing the MNE algorithms, Chebyshev spectroscopy and analysis of the noise in terms of Gaussian distribution were used.Results. The hardware im‐ plementation of the MNE method is presented. The key component of the hardware complex is presented by an autonomous microprocessor 3D seismic module. The seismic module registers signals across the frequency range of 0.5‐40 Hz with a level of spectral density of self‐noise not higher than 0.5 nm×Hz‐1/2. Presented both in land and sea design, the module is compact and mobile.Conclusion. The application of the MNE method in prospecting and exploration allows identification and exclusion of obviously non‐productive wells from drilling, as well as reduc‐ tion of the total number of wells more than by twofold. For the Caspian region, this indicator is expected to be higher. As a result, the method will provide a significant reduction in the envi‐ ronmental consequences of the oil and gas industry as a whole.

Reliability index for non-normal distributions of limit state functions

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

The Relationship between Critical Thinking Disposition and Locus of Control in Pre-Service Teachers

The aim of the current research study was to examine the link between critical thinking dispositions and locus of control in pre-service teachers. The participants of this study were selected via easily accessible sampling technique. The participants consist of 347 pre-service teachers (203 female, 144 male) in Kutahya, Turkey. The Rotter Internal-External Locus of Control Scale and Critical Thinking Dispositions Scale aided in data collection. Once the data was transferred to an electronic environment and did not show a normal distribution in terms of gender and grade variables, so Mann Whitney-U test was used in order to comparing analysis and Spearman’s correlation analysis was used for examining the level of relationship between variables. According to comparison analysis, the external locus of control and critical thinking dispositions differentiated with respect to gender and grade. In correlational analysis and regression analysis, there was a negative relationship between external locus of control and critical thinking dispositions. Results were discussed by the light of the related previous studies.

English

This study is performed with 176 academicians working in the institutions related to physical education and sports at universities. It aims to analyze organizational citizenship behaviours of academic personnel about the institutions they have been working in. Descriptive survey model was used, along with demographic data like gender, marital status, academic title. “Organizational Citizenship Behaviour” scale developed by Özaslan et al. and consisting of 21 expressions was used as data collection tool to determine organizational citizenship behaviour of people. Spearman’s Correlation coefficient was calculated for the relation between scale scores in the analysis of data. In the analysis of 3 and more groups of Normally Distributed variables ANOVA test was applied. To compare 2 groups of variables which do not come from Normal Distribution in terms of scale score Mann-Whitney U test was used and to compare 3 and more groups of variables in terms of scale scores, Kruskal-Wallis H tests were used. At the end of the research, organizational citizenship behaviour of the participants and the averages related to its dimension were above normal. As a result of additionally made multi comparisons, although a significant result was not obtained between the organizational citizenship behaviour of the participants and its dimension in statistical level according to the working period in the institution, the ages, the marital status and the academic titles of the participants, several significant results were reached statistically according to their genders and administrative position in the institution. Key words: Academician, organizational citizenship behaviour, altruism, organizational virtue, conscientiousness, Sportsmanship, courtesy.

A simple algorithm for calculating values for folded normal distribution

Folded normal distribution originates from the modulus of normal distribution. In the present article, we have formulated the cumulative distribution function (cdf) of a folded normal distribution in terms of standard normal cdf and the parameters of the mother normal distribution. Although cdf values of folded normal distribution were earlier tabulated in the literature, we have shown that those values are valid for very particular situations. We have also provided a simple approach to obtain values of the parameters of the mother normal distribution from those of the folded normal distribution. These results find ample application in practice, for example, in obtaining the so-called upper and lower α-points of folded normal distribution, which, in turn, is useful in testing of the hypothesis relating to folded normal distribution and in designing process capability control chart of some process capability indices. A thorough study has been made to compare the performance of the newly developed theory to the existing ones. Some simulated as well as real-life examples have been discussed to supplement the theory developed in this article. Codes (generated by R software) for the theory developed in this article are also presented for the ease of application.

Bootstrapping Normal and Binomial Distributions

This paper examines and compares the implications of bootstrapping normal and binomial distributions. Hypothetical data set was used aided by S-plus package. Data analysis, examination, and comparison were based on their correlation coefficients and the bootstrap estimate of the standard error of plug-in correlation coefficient. Evidence shows that both distributions behave very well as seen in the fundamental theory of statistics. Also as the bootstrap level increases, the binomial gives a lower correlation coefficient (-0.07258132), against -0.1355295 in normal distribution. It is pertinent to note that the correlation coefficient is steady as the bootstrap increases.The paper therefore focuses on the performance of the standard error of plug-in correlation coefficient. Result shows that the normal distribution gives lower standard error which suggests more reliability to the plug-in estimate. Thus, this study uses the bootstrap method to demonstrate a scenario where the normality assumption becomes stronger as the bootstrap sample sizes (100, 500, and 1000) gets larger but on approximation at two decimal places, both distributions give the same statistical inference (1000: 0.14). Therefore, binomial distribution is preferred to normal distribution in terms of their correlation coefficient but the normal distribution is preferred to binomial for carrying out further analysis in parameter estimation and other statistical inference in terms of their standard error of plug-in correlation coefficient.

A computer simulation approach to evaluating bowl versus inverted bowl assembly line arrangement with variable operation times

A computer simulation model was used to evaluate a bowl versus inverted bowl assembly line arrangement for normal and exponential distributions and variances equal to 1 and 16. The model was developed on the basis of a realistic case problem and applied to a six-station assembly line. The results show that the inverted bowl is superior to the bowl arrangement for a normal distribution in terms of the total elapsed time evaluation criterion; however, with an exponential distribution, the bowl was found better than the inverted bowl for the same criterion. On the basis of the average percentage of working time and the average time in the system evaluation criteria, the bowl was found superior to the inverted bowl for a normal distribution. Similar results were obtained for an exponential distribution with a variance equal to 1, but no definitive inference could be made with a variance equal to 16.

Edgeworth expansions and normalizing transforms for inequality measures

Abstract Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O ( n − 1 ) . This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O ( n − 3 / 2 ) . We illustrate our procedure with an application to regional inequality measurement in Cote d’Ivoire.

Distribution Fitting 3. Analysis under Normality Assumption

Four sets of experimental data were investigated in terms of normal distribution and presence of outliers. The following sets of compound were investigated: blood-brain barrier partitioning (n=105), inhibitory activity of para-substituted aromatic sulfonamides (n=47), inhibition activity of taxoids (n=63), and estrogen receptor binding affinity of triphenilacrylonitriles (n=25). The normality of experimental data was tested using the following tests: Jarque-Bera, Kormogorov-Smirnov, Anderson-Darling, Chi Square and Shapiro-Wilk. The Grubbs’ test was applied for identification of outliers. The inhibitory activity of taxoids proved to be single set of compounds normal distributed according to all applied normality tests. A proper structure-activity relationships analysis must be conducted on the sample of 98 blood-brain barrier partitioning compounds, on the sample of 34 para-substituted aromatic sulfonamides, and on the sample of 22 estrogen receptor binding affinity of triphenilacrylonitriles.

Chemistry of contact allergens and irritants

Understanding the nature and causes of contact dermatitis is as much a problem of chemistry as it is of biology. Many of the characteristics of an individual's reaction to a particular chemical, whether it be an irritant or allergen or both, depend very much on that person. From a more general perspective, however, the ability of a chemical to irritate and/or sensitize is a primary function of its chemical properties. The human biological system simply responds to the nature of the chemical perturbation it perceives; thus within the human population there is normal distribution in terms of the intensity of a reaction to a defined stimulus. This article reviews the present state of knowledge regarding the relationships between the ability of a chemical to cause contact dermatitis and its physicochemical properties, with close attention paid to how this knowledge may be used in a predictive sense to assist in risk assessment.