In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For exampl...In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.展开更多
We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be c...We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.展开更多
Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-v...Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.展开更多
We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and ...We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.展开更多
“Human-elephant conflict(HEC)”,the alarming issue,in present day context has attracted the attention of environmentalists and policy makers.The rising conflict between human beings and wild elephants is common in Bu...“Human-elephant conflict(HEC)”,the alarming issue,in present day context has attracted the attention of environmentalists and policy makers.The rising conflict between human beings and wild elephants is common in Buxa Tiger Reserve(BTR)and its adjoining area in West Bengal State,India,making the area volatile.People’s attitudes towards elephant conservation activity are very crucial to get rid of HEC,because people’s proximity with wild elephants’habitat can trigger the occurrence of HEC.The aim of this study is to conduct an in-depth investigation about the association of people’s attitudes towards HEC with their locational,demographic,and socio-economic characteristics in BTR and its adjoining area by using Pearson’s bivariate chi-square test and binary logistic regression analysis.BTR is one of the constituent parts of Eastern Doors Elephant Reserve(EDER).We interviewed 500 respondents to understand their perceptions to HEC and investigated their locational,demographic,and socio-economic characteristics including location of village,gender,age,ethnicity,religion,caste,poverty level,education level,primary occupation,secondary occupation,household type,and source of firewood.The results indicate that respondents who are living in enclave forest villages(EFVs),peripheral forest villages(PFVs),corridor village(CVs),or forest and corridor villages(FCVs),mainly males,at the age of 18–48 years old,engaged with agriculture occupation,and living in kancha and mixed houses,have more likelihood to witness HEC.Besides,respondents who are illiterate or at primary education level are more likely to regard elephant as a main problematic animal around their villages and refuse to participate in elephant conservation activity.For the sake of a sustainable environment for both human beings and wildlife,people’s attitudes towards elephants must be friendly in a more prudent way,so that the two communities can live in harmony.展开更多
Huaihe River Basin(HRB) is located in China’s north-south climatic transition zone,which is very sensitive to global climate change.Based on the daily maximum temperature,minimum temperature,and precipitation data of...Huaihe River Basin(HRB) is located in China’s north-south climatic transition zone,which is very sensitive to global climate change.Based on the daily maximum temperature,minimum temperature,and precipitation data of 40 meteorological stations and nine monthly large-scale ocean-atmospheric circulation indices data during 1959–2019,we present an assessment of the spatial and temporal variations of extreme temperature and precipitation events in the HRB using nine extreme climate indices,and analyze the teleconnection relationship between extreme climate indices and large-scale ocean-atmospheric circulation indices.The results show that warm extreme indices show a significant(P < 0.05) increasing trend,while cold extreme indices(except for cold spell duration) and diurnal temperature range(DTR) show a significant decreasing trend.Furthermore,all extreme temperature indices show significant mutations during 1959-2019.Spatially,a stronger warming trend occurs in eastern HRB than western HRB,while maximum 5-d precipitation(Rx5day) and rainstorm days(R25) show an increasing trend in the southern,central,and northwestern regions of HRB.Arctic oscillation(AO),Atlantic multidecadal oscillation(AMO),and East Atlantic/Western Russia(EA/WR) have a stronger correlation with extreme climate indices compared to other circulation indices.AO and AMO(EA/WR) exhibit a significant(P < 0.05) negative(positive)correlation with frost days and diurnal temperature range.Extreme warm events are strongly correlated with the variability of AMO and EA/WR in most parts of HRB,while extreme cold events are closely related to the variability of AO and AMO in eastern HRB.In contrast,AMO,AO,and EA/WR show limited impacts on extreme precipitation events in most parts of HRB.展开更多
In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential...In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential residual Chi-square test and applies to fault detection of an integrated navigation system.The simulation result shows that the algorithm can accurately detect the fault information of global positioning system（GPS）,eliminate the influence of false alarm and missed detection on filter,and enhance fault tolerance of integrated navigation systems.展开更多
Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degrad...Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degradation mechanism of the RET is the same as the one of the normal stress condition. In order to check the consistency of two mechanisms, we conduct two enhancement tests with a missile servo system as an object of the study, and preprocess two sets of test data to establish the accelerated degradation models regarding the temperature change rate that is assumed to be the main applied stress of the servo system during the natural storage. Based on the accelerated degradation models and natural storage profile of the servo system, we provide and demonstrate a procedure to check the consistency of two mechanisms by checking the correlation and difference of two sets of degradation data. The results indicate that the two degradation mechanisms are significantly consistent with each other.展开更多
In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the ...In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.展开更多
Knowledge on individual’s HIV/AIDS status provides a tool to reduce or avoid HIV transmission, spread and mortalities due to HIV-related illness. However, most people still do not know their HIV status because they a...Knowledge on individual’s HIV/AIDS status provides a tool to reduce or avoid HIV transmission, spread and mortalities due to HIV-related illness. However, most people still do not know their HIV status because they are not willing to test for HIV/AIDS due to various reasons. Hence the aim of this paper is to investigate the effects of various risk factors that are likely to influence decision to ever test for HIV/AIDS. The data used in this paper were obtained from the Ghana Demographic and Health Survey (n = 1828 observations and 32 risk factors). We applied the Chi-Square test statistic and the logistic regression model to the data in order to study the effects of these risk factors on one’s decision to ever test for HIV. STATA version 14.1 and R version 3.5.2 were used to carry out the statistical analyses. Generally, the results show that education, especially higher education significantly (OR = 0.53, 95% = 0.230, 0.837) increases the likelihood to ever test for HIV. Also, the younger the age groups the higher the effect and significance in the likelihood to ever test for HIV. We found that HIV-TB co-infection (OR = 0.53, 95% = 0.165, 0.893), use of condom anytime one has sex (OR = 0.31, 95% = 0.054, 0.573), wealth index (OR = 0.46, 95% = 0.137, 0.791), awareness of HIV transmission during child-delivery, number of partners significantly affect HIV testing. Those with many partners are less likely (OR = -0.26, 95% = -0.504, -0.007) to ever test for HIV and those who know that healthy person may have HIV are more likely (OR = 0.41, 95% = 0.137, 0.679) to ever test for HIV. Age is the common significant risk factor of ever tested for HIV across the 10 regions in Ghana. Resources should be allocated for more education on these significant risk factors in order to help in the fight against HIV-Health related issues.展开更多
Genetic association studies usually apply the simple chi-square (χ<sup>2</sup>)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotyp...Genetic association studies usually apply the simple chi-square (χ<sup>2</sup>)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotypes and phenotypes are independent. So, the conventional χ<sup>2</sup>-test does not consider the increased risk of an individual carrying the increasing number of disease responsible allele (a particular genotype). But, the association tests should be performed with the consideration of this disease risk according to the mode of inheritance (additive, dominant, recessive). Practical demonstration of the two possible methods for considering such order or trends in contingency tables of genetic association studies using SNP genotype data is the purpose of this paper. One method is by pooling the genotypes, and the other is scoring the individual genotypes, based on the disease risk according to the inheritance pattern. The results show that the p-values obtained from both the methods are similar for the dominant and recessive models. The other important features of the methods were also extracted using the SNP genotype data for different inheritance patterns.展开更多
文摘In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.
基金the National Natural Science Foundation of China (10571139)
文摘We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.
文摘Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.
文摘We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.
文摘“Human-elephant conflict(HEC)”,the alarming issue,in present day context has attracted the attention of environmentalists and policy makers.The rising conflict between human beings and wild elephants is common in Buxa Tiger Reserve(BTR)and its adjoining area in West Bengal State,India,making the area volatile.People’s attitudes towards elephant conservation activity are very crucial to get rid of HEC,because people’s proximity with wild elephants’habitat can trigger the occurrence of HEC.The aim of this study is to conduct an in-depth investigation about the association of people’s attitudes towards HEC with their locational,demographic,and socio-economic characteristics in BTR and its adjoining area by using Pearson’s bivariate chi-square test and binary logistic regression analysis.BTR is one of the constituent parts of Eastern Doors Elephant Reserve(EDER).We interviewed 500 respondents to understand their perceptions to HEC and investigated their locational,demographic,and socio-economic characteristics including location of village,gender,age,ethnicity,religion,caste,poverty level,education level,primary occupation,secondary occupation,household type,and source of firewood.The results indicate that respondents who are living in enclave forest villages(EFVs),peripheral forest villages(PFVs),corridor village(CVs),or forest and corridor villages(FCVs),mainly males,at the age of 18–48 years old,engaged with agriculture occupation,and living in kancha and mixed houses,have more likelihood to witness HEC.Besides,respondents who are illiterate or at primary education level are more likely to regard elephant as a main problematic animal around their villages and refuse to participate in elephant conservation activity.For the sake of a sustainable environment for both human beings and wildlife,people’s attitudes towards elephants must be friendly in a more prudent way,so that the two communities can live in harmony.
基金Under the auspices of National Natural Science Foundation of China(No.52279016,51909106,51879108,42002247,41471160)Natural Science Foundation of Guangdong Province,China(No.2020A1515011038,2020A1515111054)+1 种基金Special Fund for Science and Technology Development in 2016 of Department of Science and Technology of Guangdong Province,China(No.2016A020223007)the Project of Jinan Science and Technology Bureau(No.2021GXRC070)。
文摘Huaihe River Basin(HRB) is located in China’s north-south climatic transition zone,which is very sensitive to global climate change.Based on the daily maximum temperature,minimum temperature,and precipitation data of 40 meteorological stations and nine monthly large-scale ocean-atmospheric circulation indices data during 1959–2019,we present an assessment of the spatial and temporal variations of extreme temperature and precipitation events in the HRB using nine extreme climate indices,and analyze the teleconnection relationship between extreme climate indices and large-scale ocean-atmospheric circulation indices.The results show that warm extreme indices show a significant(P < 0.05) increasing trend,while cold extreme indices(except for cold spell duration) and diurnal temperature range(DTR) show a significant decreasing trend.Furthermore,all extreme temperature indices show significant mutations during 1959-2019.Spatially,a stronger warming trend occurs in eastern HRB than western HRB,while maximum 5-d precipitation(Rx5day) and rainstorm days(R25) show an increasing trend in the southern,central,and northwestern regions of HRB.Arctic oscillation(AO),Atlantic multidecadal oscillation(AMO),and East Atlantic/Western Russia(EA/WR) have a stronger correlation with extreme climate indices compared to other circulation indices.AO and AMO(EA/WR) exhibit a significant(P < 0.05) negative(positive)correlation with frost days and diurnal temperature range.Extreme warm events are strongly correlated with the variability of AMO and EA/WR in most parts of HRB,while extreme cold events are closely related to the variability of AO and AMO in eastern HRB.In contrast,AMO,AO,and EA/WR show limited impacts on extreme precipitation events in most parts of HRB.
基金supported by the National Natural Science Foundation of China(6063403060702066)+1 种基金the Aerospace Science Foundation(20090853013)Fundmental Research Foundation of NWPU(JC201015),Soaring Star of NWPU
文摘In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential residual Chi-square test and applies to fault detection of an integrated navigation system.The simulation result shows that the algorithm can accurately detect the fault information of global positioning system（GPS）,eliminate the influence of false alarm and missed detection on filter,and enhance fault tolerance of integrated navigation systems.
基金supported by the Natural Science Foundation of Hunan Province(2018JJ2282)
文摘Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degradation mechanism of the RET is the same as the one of the normal stress condition. In order to check the consistency of two mechanisms, we conduct two enhancement tests with a missile servo system as an object of the study, and preprocess two sets of test data to establish the accelerated degradation models regarding the temperature change rate that is assumed to be the main applied stress of the servo system during the natural storage. Based on the accelerated degradation models and natural storage profile of the servo system, we provide and demonstrate a procedure to check the consistency of two mechanisms by checking the correlation and difference of two sets of degradation data. The results indicate that the two degradation mechanisms are significantly consistent with each other.
文摘In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.
文摘Knowledge on individual’s HIV/AIDS status provides a tool to reduce or avoid HIV transmission, spread and mortalities due to HIV-related illness. However, most people still do not know their HIV status because they are not willing to test for HIV/AIDS due to various reasons. Hence the aim of this paper is to investigate the effects of various risk factors that are likely to influence decision to ever test for HIV/AIDS. The data used in this paper were obtained from the Ghana Demographic and Health Survey (n = 1828 observations and 32 risk factors). We applied the Chi-Square test statistic and the logistic regression model to the data in order to study the effects of these risk factors on one’s decision to ever test for HIV. STATA version 14.1 and R version 3.5.2 were used to carry out the statistical analyses. Generally, the results show that education, especially higher education significantly (OR = 0.53, 95% = 0.230, 0.837) increases the likelihood to ever test for HIV. Also, the younger the age groups the higher the effect and significance in the likelihood to ever test for HIV. We found that HIV-TB co-infection (OR = 0.53, 95% = 0.165, 0.893), use of condom anytime one has sex (OR = 0.31, 95% = 0.054, 0.573), wealth index (OR = 0.46, 95% = 0.137, 0.791), awareness of HIV transmission during child-delivery, number of partners significantly affect HIV testing. Those with many partners are less likely (OR = -0.26, 95% = -0.504, -0.007) to ever test for HIV and those who know that healthy person may have HIV are more likely (OR = 0.41, 95% = 0.137, 0.679) to ever test for HIV. Age is the common significant risk factor of ever tested for HIV across the 10 regions in Ghana. Resources should be allocated for more education on these significant risk factors in order to help in the fight against HIV-Health related issues.
文摘Genetic association studies usually apply the simple chi-square (χ<sup>2</sup>)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotypes and phenotypes are independent. So, the conventional χ<sup>2</sup>-test does not consider the increased risk of an individual carrying the increasing number of disease responsible allele (a particular genotype). But, the association tests should be performed with the consideration of this disease risk according to the mode of inheritance (additive, dominant, recessive). Practical demonstration of the two possible methods for considering such order or trends in contingency tables of genetic association studies using SNP genotype data is the purpose of this paper. One method is by pooling the genotypes, and the other is scoring the individual genotypes, based on the disease risk according to the inheritance pattern. The results show that the p-values obtained from both the methods are similar for the dominant and recessive models. The other important features of the methods were also extracted using the SNP genotype data for different inheritance patterns.
