scholarly journals MULTICHANNEL CONVERTION OF RANDOM DATA WITH THE PAIR-ELEMENTS OF ORDERED SAMPLES

2021 ◽  
Vol 2021 (5) ◽  
pp. 63-75
Author(s):  
R.O. Mazmanian ◽  
Keyword(s):  
Distribution Density ◽  
Single Element ◽  
Density Functions ◽  
Probability Distribution Density ◽  
Distribution Law ◽  
Random Data ◽  
Chi Square ◽  
Mutual Dependence ◽  
Structural Differences ◽  
Probability Density Function Pdf

The concept of multichannel parallel converting of probability density function (pdf) of random data was previously used for single-element pdf-converters. In development of this concept, here we investigate converting properties of spdf-converters channels formed by the sum of the ​​pairs of ordered sample elements (order statistics). The characteristics of the conversion results as dependencies on the size of the samples and the displacement of the channels relative to the median of the samples were obtained for data with a uniform distribution density. Also where excluded the areas of mutual dependence of the density functions of the summed elements, which further where normalized together with approximating them functions. Despite the apparent structural differences, the goal of this study still was to determine the closeness of the converted data with some standard functions of the probability distribution density, in particular, with the normal distribution law. As before, the estimates of the closeness of the spdf-converter channels were obtained using the chi-square criteria. The results of the research were used to determine the size and location of the statistical closeness windows, and to construct spdf-converters statistical model. References 20, figures 14.

scholarly journals NONCORRALATED DATA ORDERED SAMPLES AS A SINGLE-ELEMENT MULTICHANNEL CONVERTER

2021 ◽  
Vol 2021 (3) ◽  
pp. 74-82
Author(s):  
R.O. Mazmanian ◽  
Keyword(s):  
Normal Distribution ◽  
Statistical Testing ◽  
Random Numbers ◽  
Single Element ◽  
Data Converter ◽  
Random Data ◽  
Chi Square ◽  
Chi Square Test ◽  
Probability Density Function Pdf ◽  
Statistical Criteria

The sufficient closeness of the medians of the ordered samples of random data to the normal distribution is used in computer systems for control, monitoring and diagnosing electric power equipment. However, it remains what other probability density function (pdf) of elements (sample statistics) have such similarities. This paper presents various methods for statistical testing hypotheses for pdf-converter channels as statistics of given sizes odd numbered and ordered samples of bounded and uniformly distributed random numbers. The use of various different criteria and the results of estimates studied under the same conditions showed a sufficient conformity of the results of tests for three statistical criteria. It made possible to draw a reasonable conclusion about the preferable use of the adapted chi-square test for assessing the congruence of analytical pdf channels of the converter with normal distribution. We also suggested using the "statistical closeness window" to define those channels of the converter that do not significantly differ from the normal distribution. In addition, we presented an empirical formula determining the dependence of the size of the window of the statistical closeness window on the sample size. The results of the research are summarized in a statistical model of a multichannel uncorrelated data converter. References 27, figures 7.

F-Test Alternatives to Fisher’s Exact Test and to the Chi-Square Test of Homogeneity in 2 × 2 Tables

1983 ◽  
Vol 8 (1) ◽  
pp. 59-73 ◽  
Author(s):  
John E. Overall ◽  
Robert R. Starbuck
Keyword(s):  
Beta Distribution ◽  
Binary Response ◽  
Binomial Model ◽  
Chi Square ◽  
Exact Probability ◽  
Exact Test ◽  
Mutual Dependence ◽  
Treatment Groups ◽  
Test Of Homogeneity ◽  
Chi Square Test

A binomial model is proposed for testing the significance of differences in binary response probabilities in two independent treatment groups. Without correction for continuity, the binomial statistic is essentially equivalent to Fisher’s exact probability. With correction for continuity, the binomial statistic approaches Pearson’s chi-square. Due to mutual dependence of the binomial and F distributions on the beta distribution, a simple F statistic can be used for computation instead of the binomial.

Density functions of the bivariate chi-square distribution

1973 ◽  
Vol 2 (3) ◽  
pp. 275-288 ◽  
Author(s):  
Richard F. Gunst ◽  
John T. Webster
Keyword(s):  
Density Functions ◽  
Chi Square

Determination of Parameters of Endurance Limit Distribution Law of Material by the Methods of Nonparametric Statistics and Kinetic Theory of High-Cycle Fatigue

2017 ◽  
Vol 736 ◽  
pp. 52-57 ◽  
Author(s):  
Ksenia Syzrantseva ◽  
Vladimir Syzrantsev
Keyword(s):  
Kinetic Theory ◽  
Distribution Density ◽  
Endurance Limit ◽  
Nonparametric Statistics ◽  
Fatigue Tests ◽  
Distribution Law ◽  
Distribution Density Function ◽  
Life Tests ◽  
Determination Of Parameters

The paper considers the first developed algorithm of processing the data of specimen life tests based on the kinetic theory of mechanical fatigue and methods of nonparametric statistics. It makes it possible to determine the distribution density function of the material endurance limit. Implementation of the algorithm is illustrated on example of processing the data obtained in fatigue tests of steel 50 specimens.

Bayesian theory based software reliability demonstration test method for safety critical software

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
YUMEI WU ◽  
RISHENG YANG ◽  
HAIFENG LI ◽  
MINYA LU
Keyword(s):  
Software Reliability ◽  
Prior Distribution ◽  
Distribution Density ◽  
High Reliability ◽  
Test Method ◽  
Published Data ◽  
Density Functions ◽  
Data Sets ◽  
Safety Critical ◽  
Decreasing Functions

The original software reliability demonstration test (SRDT) does not take adequate account of prior knowledge or the prior distribution, which can lead to an expensive use of many resources. In the current paper, we propose a new improved Bayesian based SRDT method. We begin by constructing a framework for the SRDT scheme, then we use decreasing functions to construct the prior distribution density functions for both discrete and continuous safety-critical software, and then present schemes for both discrete and continuous Bayesian software demonstration functions (which we call DBSDF and CBSDF, respectively). We have carried out a set of experiments comparing our new schemes with the classic demonstration testing scheme on several published data sets. The results reveal that the DBSDF and CBSDF schemes are both more efficient and more applicable, and this is especially the case for safety-critical software with high reliability requirements.

Social Inequalities in Intimate Partner Violence: A Study of Women in Kenya

2007 ◽  
Vol 22 (6) ◽  
pp. 773-784 ◽  
Author(s):  
Stephen Lawoko ◽  
Koustuv Dalal ◽  
Luo Jiayou ◽  
Bjarne Jansson
Keyword(s):  
Intimate Partner Violence ◽  
Age Differences ◽  
Partner Violence ◽  
Social Inequalities ◽  
Occupational Status ◽  
Intimate Partner ◽  
Reproductive Age ◽  
Chi Square ◽  
Cross Sectional ◽  
Structural Differences

This study examines social inequalities in intimate partner violence (IPV) among women of reproductive age in Kenya. A sample comprising 3,696 women was retrieved from the Kenyan Demographic and Health Survey of 2003. The study design was cross-sectional. Chi-square tests and logistic regression were used to analyze the data. Results indicated that while high education among women reduced the risk of IPV exposure, both being employed and having a higher education/occupational status than her partner increased a woman’s vulnerability to IPV. Age differences between the partners, illiteracy, and lack of autonomy and access to information increased the likelihood of IPV. Finally, being in polygamous relationships was associated with IPV exposure. The findings indicate demographic, social, and structural differences in exposure to IPV with important implications for interventions.

scholarly journals A Mathematical Approximation of the Left-sided Truncated Normal Distribution Using the Cadwell Approximation Model

2017 ◽  
Vol 7 (1) ◽  
pp. 1382-1386
Author(s):  
M. M. Hamasha
Keyword(s):  
Normal Distribution ◽  
Distribution Density ◽  
Standard Normal Distribution ◽  
Maximum Deviation ◽  
Density Functions ◽  
Truncated Normal Distribution ◽  
Life Distribution ◽  
Standard Normal ◽  
Mathematical Approximation ◽  
Truncated Normal

In the case that life distribution of new devices follows the normal distribution, the life distribution of the same brand used devices follows left-sided truncated normal distribution. In spite of many mathematical models being available to approximate the normal distribution density functions, there is a few work available on modeling/approximating the density functions of left-sided truncated normal distribution. This article introduces a high accuracy mathematical model to approximate the cumulative density function of left-sided truncated standard normal distribution defined on the range of [truncation point (ZL): ∞]. The introduced model is derived from the Cadwell approximation of the normal cumulative density. The accuracy level change with Z score is discussed in details. The maximum deviation of the model results, from the real results for the whole region of [-∞<Z<-2:∞], is 0.006877.

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