The characteristics of Mann-Kendall Rank Statistics and its applications in detecting abrupt change of climate have been described.At the same time,a new method is put forward to detect the abrupt change in variance.
This article compares the size of selected subsets using nonparametric subset selection rules with two different scoring rules for the observations. The scoring rules are based on the expected values of order statisti...This article compares the size of selected subsets using nonparametric subset selection rules with two different scoring rules for the observations. The scoring rules are based on the expected values of order statistics of the uniform distribution (yielding rank values) and of the normal distribution (yielding normal score values). The comparison is made using state motor vehicle traffic fatality rates, published in a 2016 article, with fifty-one states (including DC as a state) and over a nineteen-year period (1994 through 2012). The earlier study considered four block design selection rules—two for choosing a subset to contain the “best” population (i.e., state with lowest mean fatality rate) and two for the “worst” population (i.e., highest mean rate) with a probability of correct selection chosen to be 0.90. Two selection rules based on normal scores resulted in selected subset sizes substantially smaller than corresponding rules based on ranks (7 vs. 16 and 3 vs. 12). For two other selection rules, the subsets chosen were very close in size (within one). A comparison is also made using state homicide rates, published in a 2022 article, with fifty states and covering eight years. The results are qualitatively the same as those obtained with the motor vehicle traffic fatality rates.展开更多
目的:L og rank检验是生存资料比较的标准方法,但无与之匹配的样本量测定方法。论述了这种检验的功效,为样本量研究提供依据。方法:由L ach in-Fou lkes法计算期望功效作为参照,回顾L og rank检验的3种形式,按M on te C arlo方法分别计...目的:L og rank检验是生存资料比较的标准方法,但无与之匹配的样本量测定方法。论述了这种检验的功效,为样本量研究提供依据。方法:由L ach in-Fou lkes法计算期望功效作为参照,回顾L og rank检验的3种形式,按M on te C arlo方法分别计算其观测功效,然后作对比分析。结果:所得观测功效在多数试验集均低于期望功效。与上半部相比,寿命表下半部期望和观测功效均较低。所得观测功效在不同终检水平或不同生存分布各不相同。结论:L ach in-Fou lkes法产生的样本量偏小,不能满足L og rank检验的预定功效。L og rank检验所需样本量因终检水平、生存时间或生存分布而异,L ach in-Fou lkes法无视这些事实,无法作出切合实际的测定,因此必须寻求与这种检验匹配的样本量测定方法。展开更多
A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α whi...A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α while guaranteeing the maximum power of the two constituent tests. Critical values, obtained via Monte Carlo methods, are uniformly smaller than the Bonferroni-Dunn adjustment, giving it power superiority when testing for treatment alternatives of shift in location parameter when data are sampled from non-normal distributions.展开更多
Climate change and global warming are widely recognized as the most significant environmental dilemma the world is experiencing today. Recent studies have shown that the Earth’s surface air temperature has increased ...Climate change and global warming are widely recognized as the most significant environmental dilemma the world is experiencing today. Recent studies have shown that the Earth’s surface air temperature has increased by 0.6°C - 0.8°C during the 20th century, along with changes in the hydrological cycle. This has alerted the international community and brought great interest to climate scientists leading to several studies on climate trend detection at various scales. This paper examines the long-term modification of the near surface air temperature in Rwanda. Time series of near surface air temperature data for the period ranging from 1958 to 2010 for five weather observatories were collected from the Rwanda National Meteorological Service. Variations and trends of annual mean temperature time series were examined. The cumulative sum charts (CUSUM) and bootstrapping and the sequential version of the Mann Kendall Rank Statistic were used for the detection of abrupt changes. Regression analysis was performed for the trends and the Mann-Kendall Rank Statistic Test was used for the examination of their significance. Statistically significant abrupt changes and trends have been detected. The major change point in the annual mean temperature occurred around 1977-1979. The analysis of the annual mean temperature showed for all observatories a not very significant cooling trend during the period ranging from 1958 to 1977-1979 while a significant warming trend was furthermore observed for the period after the 1977-1979 where Kigali, the Capital of Rwanda, presented the highest values of the slope (0.0455/year) with high value of coefficient of determination (R2 = 0.6798), the Kendall’s tau statistic (M-K = 0.62), the Kendall Score (S = 328) with a two-sided p-value far less than the confidence level α of 5%). This is most likely explained by the growing population and increasing urbanization and industrialization the country has experienced, especially the Capital City Kigali, during the last decades.展开更多
文摘The characteristics of Mann-Kendall Rank Statistics and its applications in detecting abrupt change of climate have been described.At the same time,a new method is put forward to detect the abrupt change in variance.
文摘This article compares the size of selected subsets using nonparametric subset selection rules with two different scoring rules for the observations. The scoring rules are based on the expected values of order statistics of the uniform distribution (yielding rank values) and of the normal distribution (yielding normal score values). The comparison is made using state motor vehicle traffic fatality rates, published in a 2016 article, with fifty-one states (including DC as a state) and over a nineteen-year period (1994 through 2012). The earlier study considered four block design selection rules—two for choosing a subset to contain the “best” population (i.e., state with lowest mean fatality rate) and two for the “worst” population (i.e., highest mean rate) with a probability of correct selection chosen to be 0.90. Two selection rules based on normal scores resulted in selected subset sizes substantially smaller than corresponding rules based on ranks (7 vs. 16 and 3 vs. 12). For two other selection rules, the subsets chosen were very close in size (within one). A comparison is also made using state homicide rates, published in a 2022 article, with fifty states and covering eight years. The results are qualitatively the same as those obtained with the motor vehicle traffic fatality rates.
文摘目的:L og rank检验是生存资料比较的标准方法,但无与之匹配的样本量测定方法。论述了这种检验的功效,为样本量研究提供依据。方法:由L ach in-Fou lkes法计算期望功效作为参照,回顾L og rank检验的3种形式,按M on te C arlo方法分别计算其观测功效,然后作对比分析。结果:所得观测功效在多数试验集均低于期望功效。与上半部相比,寿命表下半部期望和观测功效均较低。所得观测功效在不同终检水平或不同生存分布各不相同。结论:L ach in-Fou lkes法产生的样本量偏小,不能满足L og rank检验的预定功效。L og rank检验所需样本量因终检水平、生存时间或生存分布而异,L ach in-Fou lkes法无视这些事实,无法作出切合实际的测定,因此必须寻求与这种检验匹配的样本量测定方法。
文摘A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α while guaranteeing the maximum power of the two constituent tests. Critical values, obtained via Monte Carlo methods, are uniformly smaller than the Bonferroni-Dunn adjustment, giving it power superiority when testing for treatment alternatives of shift in location parameter when data are sampled from non-normal distributions.
文摘Climate change and global warming are widely recognized as the most significant environmental dilemma the world is experiencing today. Recent studies have shown that the Earth’s surface air temperature has increased by 0.6°C - 0.8°C during the 20th century, along with changes in the hydrological cycle. This has alerted the international community and brought great interest to climate scientists leading to several studies on climate trend detection at various scales. This paper examines the long-term modification of the near surface air temperature in Rwanda. Time series of near surface air temperature data for the period ranging from 1958 to 2010 for five weather observatories were collected from the Rwanda National Meteorological Service. Variations and trends of annual mean temperature time series were examined. The cumulative sum charts (CUSUM) and bootstrapping and the sequential version of the Mann Kendall Rank Statistic were used for the detection of abrupt changes. Regression analysis was performed for the trends and the Mann-Kendall Rank Statistic Test was used for the examination of their significance. Statistically significant abrupt changes and trends have been detected. The major change point in the annual mean temperature occurred around 1977-1979. The analysis of the annual mean temperature showed for all observatories a not very significant cooling trend during the period ranging from 1958 to 1977-1979 while a significant warming trend was furthermore observed for the period after the 1977-1979 where Kigali, the Capital of Rwanda, presented the highest values of the slope (0.0455/year) with high value of coefficient of determination (R2 = 0.6798), the Kendall’s tau statistic (M-K = 0.62), the Kendall Score (S = 328) with a two-sided p-value far less than the confidence level α of 5%). This is most likely explained by the growing population and increasing urbanization and industrialization the country has experienced, especially the Capital City Kigali, during the last decades.
