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 effici...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.展开更多
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’...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.展开更多
In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test s...In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.展开更多
This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q...This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q plot is used to determine the normality or otherwise of the data set. In this regards, the probabilities of the quantiles were computed, modified and plotted. Thereafter the correlation coefficients for the quantile - quantile plots were obtained. Results indicate that at 0.1 level of significance, the data for young adult males of the sample were not normally distributed, and had a mean value that is within the range of low risk, healthwise, whereas the distribution of the data for young female adults showed reasonable normality, but also with a mean value that is within the range of low risk in terms of health condition.展开更多
In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature ...In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.展开更多
One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant dif...One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant difference in the total error score (TES) between the malesand females or between the right and left eyes,but there existed some rela-tionships between the TES and age.The total error score (TES) was thelowest in the 20-29 age group and increased gradually with aging.Theanalysis of the partial...展开更多
In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditiona...In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.展开更多
We present a new nonparametric predictive inference(NPI)method using a power-normal model for accelerated life testing(ALT).Combined with the accelerating link function and imprecise probability theory,the proposed me...We present a new nonparametric predictive inference(NPI)method using a power-normal model for accelerated life testing(ALT).Combined with the accelerating link function and imprecise probability theory,the proposed method is a feasible way to predict the life of the product using ALT failure data.To validate the method,we run a series of simulations and conduct accelerated life tests with real products.The NPI lower and upper survival functions show the robustness of our method for life prediction.This is a continuous research,and some progresses have been made by updating the link function between different stress levels.We also explain how to renew and apply our model.Moreover,discussions have been made about the performance.展开更多
The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper in...The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.展开更多
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 thresho...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.展开更多
The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The...The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.展开更多
This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The ...This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The most common use of a shear test is to determine the shear strength which is the maximum shear stress that a material can withstand before the failure occurs. This parameter is useful in many engineering designs such as foundations, roads and retaining walls. We carried out an experimental laboratory test of ten samples of undisturbed soil taken at different points of the border of Wouri river of Cameroon. The samples were collected at different depths and a direct shear test was conducted. The investigations have been performed under constant vertical stresses and constant sample volume with the aim to determine the frictional angle and the cohesion of the compressible soil which are so important to establish the conditions of buildings stability. Special care was taken to derive loading conditions actually existing in the ground and to duplicate them in the laboratory. Given that the buildings constructed in this area are subjected to settlement, landslide, and punch break or shear failure, the cohesion and the frictional angle are determined through the rupture line after assessed the mean values of the shear stress for the considered ten samples. The bearing capacity of the soil, which is the fundamental soil parameter, was calculated. From the laboratory experimental results, the least squared method was used to derive an approximated mathematical model of the shearing stress. Many optimizations methods were then considered to reach the best adjustment.展开更多
文摘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.
文摘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.
基金National Natural Science Foundation of China(1047112610671176).
文摘In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.
文摘This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q plot is used to determine the normality or otherwise of the data set. In this regards, the probabilities of the quantiles were computed, modified and plotted. Thereafter the correlation coefficients for the quantile - quantile plots were obtained. Results indicate that at 0.1 level of significance, the data for young adult males of the sample were not normally distributed, and had a mean value that is within the range of low risk, healthwise, whereas the distribution of the data for young female adults showed reasonable normality, but also with a mean value that is within the range of low risk in terms of health condition.
文摘In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.
文摘One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant difference in the total error score (TES) between the malesand females or between the right and left eyes,but there existed some rela-tionships between the TES and age.The total error score (TES) was thelowest in the 20-29 age group and increased gradually with aging.Theanalysis of the partial...
文摘In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.
基金the National Natural Science Foundation of China(No.11272082)the China Scholarship Council State Scholarship Fund(No.201506070017)
文摘We present a new nonparametric predictive inference(NPI)method using a power-normal model for accelerated life testing(ALT).Combined with the accelerating link function and imprecise probability theory,the proposed method is a feasible way to predict the life of the product using ALT failure data.To validate the method,we run a series of simulations and conduct accelerated life tests with real products.The NPI lower and upper survival functions show the robustness of our method for life prediction.This is a continuous research,and some progresses have been made by updating the link function between different stress levels.We also explain how to renew and apply our model.Moreover,discussions have been made about the performance.
文摘The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.
文摘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.
文摘The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.
文摘This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The most common use of a shear test is to determine the shear strength which is the maximum shear stress that a material can withstand before the failure occurs. This parameter is useful in many engineering designs such as foundations, roads and retaining walls. We carried out an experimental laboratory test of ten samples of undisturbed soil taken at different points of the border of Wouri river of Cameroon. The samples were collected at different depths and a direct shear test was conducted. The investigations have been performed under constant vertical stresses and constant sample volume with the aim to determine the frictional angle and the cohesion of the compressible soil which are so important to establish the conditions of buildings stability. Special care was taken to derive loading conditions actually existing in the ground and to duplicate them in the laboratory. Given that the buildings constructed in this area are subjected to settlement, landslide, and punch break or shear failure, the cohesion and the frictional angle are determined through the rupture line after assessed the mean values of the shear stress for the considered ten samples. The bearing capacity of the soil, which is the fundamental soil parameter, was calculated. From the laboratory experimental results, the least squared method was used to derive an approximated mathematical model of the shearing stress. Many optimizations methods were then considered to reach the best adjustment.
