In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave o...In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave out essential details necessary for proper understanding of the individual steps. Our goal is filling in these gaps, to make our presentation accessible to advanced undergraduates. We also propose a simple formula capable of approximating the exact distribution to a sufficient accuracy for any practical sample size.展开更多
In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alter...In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.展开更多
In this article we improve a goodness-of-fit test, of the Kolmogorov-Smirnov type, for equally distributed- but not stationary-strongly dependent data. The test is based on the asymptotic behavior of the empirical pro...In this article we improve a goodness-of-fit test, of the Kolmogorov-Smirnov type, for equally distributed- but not stationary-strongly dependent data. The test is based on the asymptotic behavior of the empirical process, which is much more complex than in the classical case. Applications to simulated data and discussion of the obtained results are provided. This is, to the best of our knowledge, the first result providing a general goodness of fit test for non-weakly dependent data.展开更多
The key technology and main difficulty for optical fiber intrusion pre-warning systems （OFIPS） is the extraction of harmful-intrusion signals. After being processed by a phase-sensitive optical time-domain reflectom...The key technology and main difficulty for optical fiber intrusion pre-warning systems （OFIPS） is the extraction of harmful-intrusion signals. After being processed by a phase-sensitive optical time-domain reflectometer （O-0TDR）, vibration signals can be preliminarily extracted. Generally, these include noises and intrusions. Here, intrusions can be divided into harmful and harmless intrusions. With respect to the close study of signal characteristics, an effective extraction method of harmful intrusion is proposed in the paper. Firstly, in the part of the background reconstruction, all intrusion signals are first detected by a constant false alarm rate （CFAR）. We then reconstruct the backgrounds by extracting two-part information of alarm points, time and amplitude. This ensures that the detection background consists of intrusion signals. Secondly, in the part of the two-dimensional Kolmogorov-Smirnov （K-S） test, in order to extract harmful ones from all extracted intrusions, we design a separation method. It is based on the signal characteristics of harmful intrusion, which are shorter time interval and higher amplitude. In the actual OFIPS, the detection method is used in some typical scenes, which includes a lot of harmless intrusions, for example construction sites and busy roads. Results show that we can effectively extract harmful intrusions.展开更多
为进一步研究故障电弧特征,针对三相电动机及变频器负载开展了串联故障电弧实验。首先将电流信号经过一阶差分预处理,再通过奇异值分解SVD(singular value decomposition)对信号进行两级滤波,剔除信号中的工频和噪声成分。采用柯尔莫可...为进一步研究故障电弧特征,针对三相电动机及变频器负载开展了串联故障电弧实验。首先将电流信号经过一阶差分预处理,再通过奇异值分解SVD(singular value decomposition)对信号进行两级滤波,剔除信号中的工频和噪声成分。采用柯尔莫可洛夫-斯米洛夫K-S(Kolmogorov-Smirnov)检验法分析SVD滤波信号的正态分布情况。采用线性调频Z变换CZT(chirp-Z transform)对SVD滤波信号0~500 Hz频段进行频谱细化分析。提取时域峭度和特征频段幅值平均值组成特征向量,并构建故障电弧区矩形。通过大量数据测试表明:该方法可有效识别三相电动机及变频器负载回路中发生的故障电弧。展开更多
The empirical upper percentage points of the null distribution of a Kolmogorov-Smirnov type test for checking linearity in autoregressive models are tabulated in this paper, and the good power property of the test is ...The empirical upper percentage points of the null distribution of a Kolmogorov-Smirnov type test for checking linearity in autoregressive models are tabulated in this paper, and the good power property of the test is demonstrated.展开更多
在单接收天线下,针对频率选择性衰落信道下空时分组码(STBC)的盲识别问题,提出了一种基于Kolmogorov-Smirnov(K-S)检测的有效算法。该算法以经验累积分布函数作为特征函数,通过K-S检测经验累积分布函数之间的距离,达到识别空时分组码的...在单接收天线下,针对频率选择性衰落信道下空时分组码(STBC)的盲识别问题,提出了一种基于Kolmogorov-Smirnov(K-S)检测的有效算法。该算法以经验累积分布函数作为特征函数,通过K-S检测经验累积分布函数之间的距离,达到识别空时分组码的目的。在不同调制方式、采样因子和置信区间的条件下分别对算法进行仿真并讨论其性能,结果表明,该算法性能较好,在信噪比大于6 d B时可达到90%以上的正确识别概率,在非合作通信方面具有一定的实用价值。展开更多
The seasonal variability and spatial distribution of precipitation are the main cause of flood and drought events. The study of spatial distribution and temporal trend of precipitation in river basins has been paid mo...The seasonal variability and spatial distribution of precipitation are the main cause of flood and drought events. The study of spatial distribution and temporal trend of precipitation in river basins has been paid more and more attention. However, in China, the precipitation data are measured by weather stations （WS） of China Meteorological Administration and hydrological rain gauges （RG） of national and local hydrology bureau. The WS data usually have long record with fewer stations, while the RG data usually have short record with more stations. The consistency and correlation of these two data sets have not been well understood. In this paper, the precipitation data from 30 weather stations for 1958-2007 and 248 rain gauges for 1995-2004 in the Haihe River basin are examined and compared using linear regression, 5-year moving average, Mann-Kendall trend analysis, Kolmogorov-Smirnov test, Z test and F test methods. The results show that the annual precipitation from both WS and RG records are normally distributed with minor difference in the mean value and variance. It is statistically feasible to extend the precipitation of RG by WS data sets. Using the extended precipitation data, the detailed spatial distribution of the annual and seasonal precipitation amounts as well as their temporal trends are calculated and mapped. The various distribution maps produced in the study show that for the whole basin the precipitation of 1958-2007 has been decreasing except for spring season. The decline trend is significant in summer, and this trend is stronger after the 1980s. The annual and seasonal precipitation amounts and changing trends are different in different regions and seasons. The precipitation is decreasing from south to north, from coastal zone to inland area.展开更多
Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibili...Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.展开更多
Chronic disease is an important factor that affect the health of elderly people. We analyzed the 2006 and 2010 data from the Chinese Urban and Rural Elderly Population Surveys, which are nationally representative surv...Chronic disease is an important factor that affect the health of elderly people. We analyzed the 2006 and 2010 data from the Chinese Urban and Rural Elderly Population Surveys, which are nationally representative surveys of elderly people aged 60 years and above. We found that there existed a typical power-law distribution for the rates of different numbers of chronic diseases among elderly Chinese people. A Kolmogorov-Smirnov test indicated that the result was robust, and the power exponents were approximately ?2.5. In addition, a paired t-test was conducted, which demonstrated that the rates of different numbers of chronic diseases did not have significant urban-rural differences, time differences or gender differences.展开更多
This paper presents a minimum error thresholding (MET) algorithm under the hypothesis that the gray level histogram of SAR image fits to a mixture model of shifted Rayleigh distribution. This algorithm is applied to r...This paper presents a minimum error thresholding (MET) algorithm under the hypothesis that the gray level histogram of SAR image fits to a mixture model of shifted Rayleigh distribution. This algorithm is applied to real SAR images and compared with traditional Otsu algorithm and other MET algorithms based on various models of histogram. The hypothesis of using Rayleigh distribution model is confirmed by Kolmogorov-Smirnov testing and the comparison results obtained show that the proposed new algorithm has good performance in thresholding SAR images.展开更多
Tourism impacts on society are complex and mixed.However,they are vital to diverse societies,clusters,and individuals dependent upon their morals,attitudes,and resources existing for tourism development.Increasing tou...Tourism impacts on society are complex and mixed.However,they are vital to diverse societies,clusters,and individuals dependent upon their morals,attitudes,and resources existing for tourism development.Increasing tourism also brings many problems.Hence,tourist experience is fundamental for destination image and devel-opment.This research examines tourist perceptions and attitudes toward tourism impacts in Chitkul,Kalpa,and Nako in Kinnaur.Random sampling has been used to measure tourist responses on a range of indicators related to tourism development.Likert scale responses were analyzed using factor analysis,ANOVA,Mann-Whitney U-test,Kolmogorov test,and descriptive statistics.The results confirmed that tourists do not perceive any type of pollu-tion or societal barriers.They observed that natural magnetism and the socio-cultural milieu of the destination is what attracts tourists.However,tourists are not satisfied with‘networking services’,‘organization efforts’,‘sup-plementary conveniences’,and‘carriage concerns’at selected destinations in Kinnaur.Moreover,Chitkul emerged as the top tourist destination in Kinnaur.Since the destination would emerge as a hub of tourist activities shortly considering the congestion and exploitation of nearby tourist destinations at Kulu-Manali-Rohtang in Beas Valley.Hence,the assessment of tourist perceptions can be used as an indicator of tourism destination competitiveness and can assist in developing appropriate tourism policies and infrastructure upgrades.展开更多
The World Wide Web is essential to general public nowadays. From a data analysis viewpoint, it provides rich opportunities to gather observational data on a large-scale. This paper focuses on modeling the behavior of ...The World Wide Web is essential to general public nowadays. From a data analysis viewpoint, it provides rich opportunities to gather observational data on a large-scale. This paper focuses on modeling the behavior of visitors to an academic website. Although the conventional probability models, which were used by other literature for fitting in a commercial web site, capture the power law behavior in our data, they fail to capture other important features like the long tail. We propose a new model based on the identities of the users. Qualitative and quantitative tests, which are used for comparing the model fitting to our data, show that the new model outperforms other two conventional probability models.展开更多
文摘In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave out essential details necessary for proper understanding of the individual steps. Our goal is filling in these gaps, to make our presentation accessible to advanced undergraduates. We also propose a simple formula capable of approximating the exact distribution to a sufficient accuracy for any practical sample size.
文摘In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.
文摘In this article we improve a goodness-of-fit test, of the Kolmogorov-Smirnov type, for equally distributed- but not stationary-strongly dependent data. The test is based on the asymptotic behavior of the empirical process, which is much more complex than in the classical case. Applications to simulated data and discussion of the obtained results are provided. This is, to the best of our knowledge, the first result providing a general goodness of fit test for non-weakly dependent data.
文摘The key technology and main difficulty for optical fiber intrusion pre-warning systems （OFIPS） is the extraction of harmful-intrusion signals. After being processed by a phase-sensitive optical time-domain reflectometer （O-0TDR）, vibration signals can be preliminarily extracted. Generally, these include noises and intrusions. Here, intrusions can be divided into harmful and harmless intrusions. With respect to the close study of signal characteristics, an effective extraction method of harmful intrusion is proposed in the paper. Firstly, in the part of the background reconstruction, all intrusion signals are first detected by a constant false alarm rate （CFAR）. We then reconstruct the backgrounds by extracting two-part information of alarm points, time and amplitude. This ensures that the detection background consists of intrusion signals. Secondly, in the part of the two-dimensional Kolmogorov-Smirnov （K-S） test, in order to extract harmful ones from all extracted intrusions, we design a separation method. It is based on the signal characteristics of harmful intrusion, which are shorter time interval and higher amplitude. In the actual OFIPS, the detection method is used in some typical scenes, which includes a lot of harmless intrusions, for example construction sites and busy roads. Results show that we can effectively extract harmful intrusions.
文摘为进一步研究故障电弧特征,针对三相电动机及变频器负载开展了串联故障电弧实验。首先将电流信号经过一阶差分预处理,再通过奇异值分解SVD(singular value decomposition)对信号进行两级滤波,剔除信号中的工频和噪声成分。采用柯尔莫可洛夫-斯米洛夫K-S(Kolmogorov-Smirnov)检验法分析SVD滤波信号的正态分布情况。采用线性调频Z变换CZT(chirp-Z transform)对SVD滤波信号0~500 Hz频段进行频谱细化分析。提取时域峭度和特征频段幅值平均值组成特征向量,并构建故障电弧区矩形。通过大量数据测试表明:该方法可有效识别三相电动机及变频器负载回路中发生的故障电弧。
基金a Grant from the Natural Sciences and Engineering Research Council of Canada. This research is supported in part by the Nation
文摘The empirical upper percentage points of the null distribution of a Kolmogorov-Smirnov type test for checking linearity in autoregressive models are tabulated in this paper, and the good power property of the test is demonstrated.
文摘在单接收天线下,针对频率选择性衰落信道下空时分组码(STBC)的盲识别问题,提出了一种基于Kolmogorov-Smirnov(K-S)检测的有效算法。该算法以经验累积分布函数作为特征函数,通过K-S检测经验累积分布函数之间的距离,达到识别空时分组码的目的。在不同调制方式、采样因子和置信区间的条件下分别对算法进行仿真并讨论其性能,结果表明,该算法性能较好,在信噪比大于6 d B时可达到90%以上的正确识别概率,在非合作通信方面具有一定的实用价值。
基金National Basic Research Program of China, No.2010CB428406 The Key Knowledge Innovation Project of the CAS, No.KZCX2-YW-126 Key Project of National Natural Science Foundation of China, No.40730632
文摘The seasonal variability and spatial distribution of precipitation are the main cause of flood and drought events. The study of spatial distribution and temporal trend of precipitation in river basins has been paid more and more attention. However, in China, the precipitation data are measured by weather stations （WS） of China Meteorological Administration and hydrological rain gauges （RG） of national and local hydrology bureau. The WS data usually have long record with fewer stations, while the RG data usually have short record with more stations. The consistency and correlation of these two data sets have not been well understood. In this paper, the precipitation data from 30 weather stations for 1958-2007 and 248 rain gauges for 1995-2004 in the Haihe River basin are examined and compared using linear regression, 5-year moving average, Mann-Kendall trend analysis, Kolmogorov-Smirnov test, Z test and F test methods. The results show that the annual precipitation from both WS and RG records are normally distributed with minor difference in the mean value and variance. It is statistically feasible to extend the precipitation of RG by WS data sets. Using the extended precipitation data, the detailed spatial distribution of the annual and seasonal precipitation amounts as well as their temporal trends are calculated and mapped. The various distribution maps produced in the study show that for the whole basin the precipitation of 1958-2007 has been decreasing except for spring season. The decline trend is significant in summer, and this trend is stronger after the 1980s. The annual and seasonal precipitation amounts and changing trends are different in different regions and seasons. The precipitation is decreasing from south to north, from coastal zone to inland area.
文摘Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.
文摘Chronic disease is an important factor that affect the health of elderly people. We analyzed the 2006 and 2010 data from the Chinese Urban and Rural Elderly Population Surveys, which are nationally representative surveys of elderly people aged 60 years and above. We found that there existed a typical power-law distribution for the rates of different numbers of chronic diseases among elderly Chinese people. A Kolmogorov-Smirnov test indicated that the result was robust, and the power exponents were approximately ?2.5. In addition, a paired t-test was conducted, which demonstrated that the rates of different numbers of chronic diseases did not have significant urban-rural differences, time differences or gender differences.
基金Supported by the National Natural Foundation of China(No.69672029 and No.69772021)
文摘This paper presents a minimum error thresholding (MET) algorithm under the hypothesis that the gray level histogram of SAR image fits to a mixture model of shifted Rayleigh distribution. This algorithm is applied to real SAR images and compared with traditional Otsu algorithm and other MET algorithms based on various models of histogram. The hypothesis of using Rayleigh distribution model is confirmed by Kolmogorov-Smirnov testing and the comparison results obtained show that the proposed new algorithm has good performance in thresholding SAR images.
文摘Tourism impacts on society are complex and mixed.However,they are vital to diverse societies,clusters,and individuals dependent upon their morals,attitudes,and resources existing for tourism development.Increasing tourism also brings many problems.Hence,tourist experience is fundamental for destination image and devel-opment.This research examines tourist perceptions and attitudes toward tourism impacts in Chitkul,Kalpa,and Nako in Kinnaur.Random sampling has been used to measure tourist responses on a range of indicators related to tourism development.Likert scale responses were analyzed using factor analysis,ANOVA,Mann-Whitney U-test,Kolmogorov test,and descriptive statistics.The results confirmed that tourists do not perceive any type of pollu-tion or societal barriers.They observed that natural magnetism and the socio-cultural milieu of the destination is what attracts tourists.However,tourists are not satisfied with‘networking services’,‘organization efforts’,‘sup-plementary conveniences’,and‘carriage concerns’at selected destinations in Kinnaur.Moreover,Chitkul emerged as the top tourist destination in Kinnaur.Since the destination would emerge as a hub of tourist activities shortly considering the congestion and exploitation of nearby tourist destinations at Kulu-Manali-Rohtang in Beas Valley.Hence,the assessment of tourist perceptions can be used as an indicator of tourism destination competitiveness and can assist in developing appropriate tourism policies and infrastructure upgrades.
文摘The World Wide Web is essential to general public nowadays. From a data analysis viewpoint, it provides rich opportunities to gather observational data on a large-scale. This paper focuses on modeling the behavior of visitors to an academic website. Although the conventional probability models, which were used by other literature for fitting in a commercial web site, capture the power law behavior in our data, they fail to capture other important features like the long tail. We propose a new model based on the identities of the users. Qualitative and quantitative tests, which are used for comparing the model fitting to our data, show that the new model outperforms other two conventional probability models.
