The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wo...The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n<sub>0</sub> (number of zeros) and n<sub>1</sub> (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.展开更多
Analysis of carcinogenicity data generally involves a trend test across all dose groups and a pairwise comparison of the high dose group with the control. The most commonly used test for a positive trend is the Cochra...Analysis of carcinogenicity data generally involves a trend test across all dose groups and a pairwise comparison of the high dose group with the control. The most commonly used test for a positive trend is the Cochran-Armitage test. This test is asymptotically normal. For the pairwise comparison of the high dose group with the control group, we propose two modifications: the first modification is to apply the test on the data from high dose and control groups after dropping the data from the low and the medium dose groups;the second modification is to adjust the test conditional on data from all dose groups. We compare the power performance of these two modifications for the pairwise comparisons.展开更多
According to the assumption of slightly compressible fluid, the quadraticgradient term in the nonlinear partial differential equations for the traditional well-test model isusually neglected. The linear partial differ...According to the assumption of slightly compressible fluid, the quadraticgradient term in the nonlinear partial differential equations for the traditional well-test model isusually neglected. The linear partial differential equation is thus established. It is known thatneglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flowmodel for fractal medium is constructed and the quadratic gradient term is considered. The exactsolutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in aconstant-rate and constant-pressure production for an infinitely large system. This paper addressesthe variation of pressure with fluid compressibility coefficient and fractal reservoir parameters.The plots of the typical pressure curves are constructed, and the results can be applied towell-test analysis.展开更多
Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the...Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.展开更多
A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the non...A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.展开更多
Applied statisticians are often confronted with statistical inference problems dealing with situations in which there appear to be no data,or data of only limited usefulness.For example,when attempting to find a confi...Applied statisticians are often confronted with statistical inference problems dealing with situations in which there appear to be no data,or data of only limited usefulness.For example,when attempting to find a confidence interval for a binomial proportion,the sample may contain no successes.Such a scenario could be encountered when attempting to estimate the incidence of an extremely rare side effect associated with the administration of a newly developed drug.In this article,we use examples for our experiences working with scientific investigators and describe several scenarios in which there appeared to be no useful data,or data of only limited usefulness.We describe the methods we prefer for analyzing the data in these situations and illustrate their application using the actual data from the investigations we participated in.展开更多
文摘The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n<sub>0</sub> (number of zeros) and n<sub>1</sub> (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.
文摘Analysis of carcinogenicity data generally involves a trend test across all dose groups and a pairwise comparison of the high dose group with the control. The most commonly used test for a positive trend is the Cochran-Armitage test. This test is asymptotically normal. For the pairwise comparison of the high dose group with the control group, we propose two modifications: the first modification is to apply the test on the data from high dose and control groups after dropping the data from the low and the medium dose groups;the second modification is to adjust the test conditional on data from all dose groups. We compare the power performance of these two modifications for the pairwise comparisons.
文摘According to the assumption of slightly compressible fluid, the quadraticgradient term in the nonlinear partial differential equations for the traditional well-test model isusually neglected. The linear partial differential equation is thus established. It is known thatneglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flowmodel for fractal medium is constructed and the quadratic gradient term is considered. The exactsolutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in aconstant-rate and constant-pressure production for an infinitely large system. This paper addressesthe variation of pressure with fluid compressibility coefficient and fractal reservoir parameters.The plots of the typical pressure curves are constructed, and the results can be applied towell-test analysis.
基金Beijing Natural Science Foundation(Grant No.Z200001)National Natural Science Foundation of China(Grant Nos.11871001,11971478 and 11971001)the Fundamental Research Funds for the Central Universities(Grant No.2019NTSS18)。
文摘Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675084 and 11435005Ningbo Natural Science Foundation under Grant No.2015A610159+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.
文摘Applied statisticians are often confronted with statistical inference problems dealing with situations in which there appear to be no data,or data of only limited usefulness.For example,when attempting to find a confidence interval for a binomial proportion,the sample may contain no successes.Such a scenario could be encountered when attempting to estimate the incidence of an extremely rare side effect associated with the administration of a newly developed drug.In this article,we use examples for our experiences working with scientific investigators and describe several scenarios in which there appeared to be no useful data,or data of only limited usefulness.We describe the methods we prefer for analyzing the data in these situations and illustrate their application using the actual data from the investigations we participated in.
