This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviat...This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.展开更多
When the population, from which the samples are extracted, is not normally distributed, or if the sample size is particularly reduced, become preferable the use of not parametric statistic test. An alternative to the ...When the population, from which the samples are extracted, is not normally distributed, or if the sample size is particularly reduced, become preferable the use of not parametric statistic test. An alternative to the normal model is the permutation or randomization model. The permutation model is nonparametric because no formal assumptions are made about the population parameters of the reference distribution, i.e., the distribution to which an obtained result is compared to determine its probability when the null hypothesis is true. Typically the reference distribution is a sampling distribution for parametric tests and a permutation distribution for many nonparametric tests. Within the regression models, it is possible to use the permutation tests, considering their ownerships of optimality, especially in the multivariate context and the normal distribution of the response variables is not guaranteed. In the literature there are numerous permutation tests applicable to the estimation of the regression models. The purpose of this study is to examine different kinds of permutation tests applied to linear models, focused our attention on the specific test statistic on which they are based. In this paper we focused our attention on permutation test of the independent variables, proposed by Oja, and other methods to effect the inference in non parametric way, in a regression model. Moreover, we show the recent advances in this context and try to compare them.展开更多
The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource devel...The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource development, and hydropower system reliability in the region rely heavily on monsoon rainfall. Monthly rainfall data from three stations (East Nimar, Barwani, and West Nimar) were analyzed. Initially, the pre-whitening method was applied to eliminate serial correlation effects from the rainfall data series. Subsequently, statistical trends in annual and seasonal rainfall were assessed using both parametric (student-t test) and non-parametric tests [Mann-Kendall, Sen’s slope estimator, and Cumulative Sum (CUSUM)]. The magnitude of the rainfall trend was determined using Theil-Sen’s slope estimator. Spatial analysis of the Mann-Kendall test on an annual basis revealed a statistically insignificant decreasing trend for Barwani and East Nimar and an increasing trend for West Nimar. On a seasonal basis, the monsoon season contributes a significant percentage (88.33%) to the total annual rainfall. The CUSUM test results indicated a shift change detection in annual rainfall data for Barwani in 1997, while shifts were observed in West and East Nimar stations in 1929. These findings offer valuable insights into regional rainfall behavior, aiding in the planning and management of water resources and ecological systems.展开更多
Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In mos...Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.展开更多
在快速城市化的长江三角洲地区,植被覆盖状况变化问题已经引起公众的关注并且成为科学研究的热点。植被指数作为监测植被和生态环境变化的有效指标而得到广泛应用。基于2000—2011年的Terra Modis NDVI植被指数数据集,从时间尺度和空间...在快速城市化的长江三角洲地区,植被覆盖状况变化问题已经引起公众的关注并且成为科学研究的热点。植被指数作为监测植被和生态环境变化的有效指标而得到广泛应用。基于2000—2011年的Terra Modis NDVI植被指数数据集,从时间尺度和空间变化上分析长江三角洲地区植被变化特征,应用一元线性回归趋势分析方法和更适合研究非正态分布数据的Mann-Kendall非参数检验方法对长江三角洲地区的植被覆盖状况进行研究。研究结果表明,(1)利用Terra Modis NDVI数据可以很好地从宏观上监测长江三角洲地区植被覆盖的时空变化。(2)植被覆盖的时空变化是自然和人类活动共同作用的结果,特别是在快速城市化的长江三角洲地区,人类活动对植被覆盖的影响更为剧烈,并且植被覆盖变化对人类活动做出积极的响应。12年来,长江三角洲地区植被覆盖总体呈下降趋势,尤其是研究区中的城市及周边地区则以显著下降趋势为主,说明长江三角洲地区随着城市化进程的加速,植被覆盖状况正面临着恶化。(3)一元线性回归趋势分析方法和Mann-Kendall非参数检验方法对植被变化趋势的检测总体上趋于一致,两者可以相互印证,但局部有差异。因此,当进行局部区域植被覆盖变化的深入研究及驱动力分析时,需要较高分辨率的数据作为辅助数据。研究揭示了快速城市化背景下长江三角洲地区植被覆盖变化的规律,从而为长江三角洲地区生态保护和植被恢复提供有利的依据和借鉴。展开更多
文摘This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.
文摘When the population, from which the samples are extracted, is not normally distributed, or if the sample size is particularly reduced, become preferable the use of not parametric statistic test. An alternative to the normal model is the permutation or randomization model. The permutation model is nonparametric because no formal assumptions are made about the population parameters of the reference distribution, i.e., the distribution to which an obtained result is compared to determine its probability when the null hypothesis is true. Typically the reference distribution is a sampling distribution for parametric tests and a permutation distribution for many nonparametric tests. Within the regression models, it is possible to use the permutation tests, considering their ownerships of optimality, especially in the multivariate context and the normal distribution of the response variables is not guaranteed. In the literature there are numerous permutation tests applicable to the estimation of the regression models. The purpose of this study is to examine different kinds of permutation tests applied to linear models, focused our attention on the specific test statistic on which they are based. In this paper we focused our attention on permutation test of the independent variables, proposed by Oja, and other methods to effect the inference in non parametric way, in a regression model. Moreover, we show the recent advances in this context and try to compare them.
文摘The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource development, and hydropower system reliability in the region rely heavily on monsoon rainfall. Monthly rainfall data from three stations (East Nimar, Barwani, and West Nimar) were analyzed. Initially, the pre-whitening method was applied to eliminate serial correlation effects from the rainfall data series. Subsequently, statistical trends in annual and seasonal rainfall were assessed using both parametric (student-t test) and non-parametric tests [Mann-Kendall, Sen’s slope estimator, and Cumulative Sum (CUSUM)]. The magnitude of the rainfall trend was determined using Theil-Sen’s slope estimator. Spatial analysis of the Mann-Kendall test on an annual basis revealed a statistically insignificant decreasing trend for Barwani and East Nimar and an increasing trend for West Nimar. On a seasonal basis, the monsoon season contributes a significant percentage (88.33%) to the total annual rainfall. The CUSUM test results indicated a shift change detection in annual rainfall data for Barwani in 1997, while shifts were observed in West and East Nimar stations in 1929. These findings offer valuable insights into regional rainfall behavior, aiding in the planning and management of water resources and ecological systems.
文摘Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.
文摘在快速城市化的长江三角洲地区,植被覆盖状况变化问题已经引起公众的关注并且成为科学研究的热点。植被指数作为监测植被和生态环境变化的有效指标而得到广泛应用。基于2000—2011年的Terra Modis NDVI植被指数数据集,从时间尺度和空间变化上分析长江三角洲地区植被变化特征,应用一元线性回归趋势分析方法和更适合研究非正态分布数据的Mann-Kendall非参数检验方法对长江三角洲地区的植被覆盖状况进行研究。研究结果表明,(1)利用Terra Modis NDVI数据可以很好地从宏观上监测长江三角洲地区植被覆盖的时空变化。(2)植被覆盖的时空变化是自然和人类活动共同作用的结果,特别是在快速城市化的长江三角洲地区,人类活动对植被覆盖的影响更为剧烈,并且植被覆盖变化对人类活动做出积极的响应。12年来,长江三角洲地区植被覆盖总体呈下降趋势,尤其是研究区中的城市及周边地区则以显著下降趋势为主,说明长江三角洲地区随着城市化进程的加速,植被覆盖状况正面临着恶化。(3)一元线性回归趋势分析方法和Mann-Kendall非参数检验方法对植被变化趋势的检测总体上趋于一致,两者可以相互印证,但局部有差异。因此,当进行局部区域植被覆盖变化的深入研究及驱动力分析时,需要较高分辨率的数据作为辅助数据。研究揭示了快速城市化背景下长江三角洲地区植被覆盖变化的规律,从而为长江三角洲地区生态保护和植被恢复提供有利的依据和借鉴。
