In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fi...In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.展开更多
This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests p...This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.展开更多
We investigate redshift distributions of three long burst samples, with the first sample containing 131 long bursts with observed redshifts, the second including 220 long bursts with pseudo-redshifts calculated by the...We investigate redshift distributions of three long burst samples, with the first sample containing 131 long bursts with observed redshifts, the second including 220 long bursts with pseudo-redshifts calculated by the variability-luminosity relation, and the third including 1194 long bursts with pseudo-redshifls calculated by the lag-luminosity relation, respectively. In the redshift range 0-1 the Kolmogorov-Smirnov probability of the observed redshift distribution and that of the variability-luminosity relation is large. In the redshift ranges 1-2, 2-3, 3-6.3 and 0-37, the Kolmogorov-Smirnov probabilities of the redshift distribution from lag-luminosity relation and the observed redshift distribution are also large. For the GRBs, which appear both in the two pseudo-redshift burst samples, the KS probability of the pseudo-redshift distribution from the lag-luminosity relation and the observed reshift distribution is 0.447, which is very large. Based on these results, some conclusions are drawn： i） the V-Liso relation might be more believable than the τ-Liso relation in low redshift ranges and the τ-Liso relation might be more real than the V-Liso relation in high redshift ranges; ii） if we do not consider the redshift ranges, the τ-Liso relation might be more physical and intrinsical than the V-Liso relation.展开更多
This study explores the arrivals of water pipeline break failures. The aim is to assist the facility manager in the decision making process. Based on characteristics of the data set ranging from 2011 to 2014, two step...This study explores the arrivals of water pipeline break failures. The aim is to assist the facility manager in the decision making process. Based on characteristics of the data set ranging from 2011 to 2014, two steps of analysis were presented in the paper. This first step is the analysis of partially complete data set (2011 data). The 2-sample KS test is adopted to check the similarity between this data set and the entire data set with no underlying distribution implied. In order to conduct the reliability analysis, the Weibull distribution is adopted to evaluate the data. For annual data set, the 2-parameter Weibull distribution fits data sets pretty well. The shape parameters are a little greater than 1, indicating a slightly increasing arrival rate of such failures. For the entire data set, the 3-parameter Weibull tends to fit the data better than the 2-parameter Weibull. The shape parameter is well above 1, indicating an increasing arrival rate of the failures. To eliminate the impact of missing points for the 2011 data set, data from 2012 to 2014 were also considered as a new set, the Weibull distribution generated a decent fitting. The shape parameter is a little greater than 1. Therefore, there is a slightly increasing arrival rate of those pipeline failures. Results from this study provide decision makers valuable information in terms of whether additional efforts shall be made to enhance the system’s performance in order to reduce the failure rate.展开更多
A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall rev...A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.展开更多
文摘In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.
文摘This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.
基金supported by the National Natural Science Foundation of China(NSFC, No. 10473023)Scientific Research Fund of the Sichuan Provincial Education Department,the K. C. Wong Education Foundation (Hong Kong)the Jiangsu Planned Projects for PostdoctoralResearch Funds.
文摘We investigate redshift distributions of three long burst samples, with the first sample containing 131 long bursts with observed redshifts, the second including 220 long bursts with pseudo-redshifts calculated by the variability-luminosity relation, and the third including 1194 long bursts with pseudo-redshifls calculated by the lag-luminosity relation, respectively. In the redshift range 0-1 the Kolmogorov-Smirnov probability of the observed redshift distribution and that of the variability-luminosity relation is large. In the redshift ranges 1-2, 2-3, 3-6.3 and 0-37, the Kolmogorov-Smirnov probabilities of the redshift distribution from lag-luminosity relation and the observed redshift distribution are also large. For the GRBs, which appear both in the two pseudo-redshift burst samples, the KS probability of the pseudo-redshift distribution from the lag-luminosity relation and the observed reshift distribution is 0.447, which is very large. Based on these results, some conclusions are drawn： i） the V-Liso relation might be more believable than the τ-Liso relation in low redshift ranges and the τ-Liso relation might be more real than the V-Liso relation in high redshift ranges; ii） if we do not consider the redshift ranges, the τ-Liso relation might be more physical and intrinsical than the V-Liso relation.
文摘This study explores the arrivals of water pipeline break failures. The aim is to assist the facility manager in the decision making process. Based on characteristics of the data set ranging from 2011 to 2014, two steps of analysis were presented in the paper. This first step is the analysis of partially complete data set (2011 data). The 2-sample KS test is adopted to check the similarity between this data set and the entire data set with no underlying distribution implied. In order to conduct the reliability analysis, the Weibull distribution is adopted to evaluate the data. For annual data set, the 2-parameter Weibull distribution fits data sets pretty well. The shape parameters are a little greater than 1, indicating a slightly increasing arrival rate of such failures. For the entire data set, the 3-parameter Weibull tends to fit the data better than the 2-parameter Weibull. The shape parameter is well above 1, indicating an increasing arrival rate of the failures. To eliminate the impact of missing points for the 2011 data set, data from 2012 to 2014 were also considered as a new set, the Weibull distribution generated a decent fitting. The shape parameter is a little greater than 1. Therefore, there is a slightly increasing arrival rate of those pipeline failures. Results from this study provide decision makers valuable information in terms of whether additional efforts shall be made to enhance the system’s performance in order to reduce the failure rate.
文摘A saddlepoint approximation for a two-sample permutation test was obtained by Robinson[7].Although the approximation is very accurate, the formula is very complicated and difficult toapply. In this papert we shall revisit the same problem from a different angle. We shall first turnthe problem into a conditional probability and then apply a Lugannani-Rice type formula to it,which was developed by Skovagard[8] for the mean of i.i.d. samples and by Jing and Robinson[5]for smooth function of vector means. Both the Lugannani-Rice type formula and Robinson'sformula achieve the same relative error of order O(n-3/2), but the former is very compact andmuch easier to use in practice. Some numerical results will be presented to compare the twoformulas.
