Applications of Normality Test in Statistical Analysis

In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.

Wigner-Matrix-Based Normality Test and Application to Weak Signal Detection in SISO/SIMO Systems

Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.

Testing for Normality from the Parametric Seven-Number Summary

The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.

Speaker Verification Based on Log-Likelihood Score Normalization

Due to differences in the distribution of scores for different trials, the performance of a speaker verification system will be seriously diminished if raw scores are directly used for detection with a unified threshold value. As such, the scores must be normalized. To tackle the shortcomings of score normalization methods, we propose a speaker verification system based on log-likelihood normalization (LLN). Without a priori knowledge, LLN increases the separation between scores of target and non-target speaker models, so as to improve score aliasing of “same-speaker” and “different-speaker” trials corresponding to the same test speech, enabling better discrimination and decision capability. The experiment shows that LLN is an effective method of scoring normalization.

Polynomial Tests of Normal Forms and Some Related Results

The following problem is called the everywhere-cover problem:“Given a set of dependencies over a database scheme,is the set of dependencies explicitly given for each relation scheme equivalent to the dependencies implied for that relation scheme?”It is shown that when the everywhere-cover problem has a ‘yes’ answer,examining only the dependencies explicitly given will suffice to test 3NF,BCNF and 4NF of a database scheme.But this does not hold for 2NF.Consequently,in such cases,tests of BCNF and 4NF all take polynomial time.Then a proof is given that test of 3NF of a database scheme is Co-NP-complete,and from this result it is shown that everywhere-cover is also Co-NP-complete when only functional dependencies are allowed.These results lead to doubt the truth of the well believed conjec- ture that no polynomial time algorithm for designing a Iossless BCNF database scheme is likely to exist.

Quantitative characterization of horizontal well production performance with multiple indicators: a case study on the Weiyuan shale gas field in the Sichuan Basin, China

To quantitatively characterize the horizontal shale gas well productivity and identify the dominant productivity factors in the Weiyuan Shale Gas Field,Sichuan Basin,a practical productivity method involving multiple indicators was proposed to analyze the production performance of 150 horizontal wells.The normalized test production,flowback ratio,first-year initial production and estimated/expected ultimate recovery(EUR)were introduced to estimate the well productivity in different production stages.The correlation between these four indicators was determined to reveal their effects on production performance forecasts.In addition,the dominant productivity factors in the present stage were identified to provide guidance for production performance enhancement.Research indicates that favorable linear relations exist between the normalized test production,first-year initial production and EUR.The normalized test production is regarded as an important indicator to preliminarily characterize the well productivity in the initial stage.The first-year initial production is the most accurate productivity evaluation indicator after a year.The flowback ratio is a supplementary indicator that qualitatively represents the well productivity and fracturing performance.The well productivity is greatly dependent on the lateral target interval,drilling length of Longmaxi1_(1)^(1)(LM1_(1)^(1))and wellbore integrity.The first-year recovery degree of EUR is 24%–58%with a P50 value of 35%.

Advances in SVM-Based System Using GMM Super Vectors for Text-Independent Speaker Verification

For text-independent speaker verification, the Gaussian mixture model （GMM） using a universal background model strategy and the GMM using support vector machines are the two most commonly used methodologies. Recently, a new SVM-based speaker verification method using GMM super vectors has been proposed. This paper describes the construction of a new speaker verification system and investigates the use of nuisance attribute projection and test normalization to further enhance performance. Experiments were conducted on the core test of the 2006 NIST speaker recognition evaluation corpus. The experimental results indicate that an SVM-based speaker verification system using GMM super vectors can achieve appealing performance. With the use of nuisance attribute projection and test normalization, the system performance can be significantly improved, with improvements in the equal error rate from 7.78% to 4.92% and detection cost function from 0.0376 to 0.0251.