Extreme value theory provides methods to analyze the most extreme parts of data. We predicted the ultimate 100 m dash records for men and women for specific periods using the generalized extreme value (GEV) distributi...Extreme value theory provides methods to analyze the most extreme parts of data. We predicted the ultimate 100 m dash records for men and women for specific periods using the generalized extreme value (GEV) distribution. The various diagnostic plots, which assessed the accuracy of the GEV model, were well fitted to the 100 m records in the world and Japan, validating the model. The men’s world record had a shape parameter of -0.250 with a 95% confidence interval of [-0.391, -0.109]. The 100 m record had a finite limit and a calculated upper limit was 9.46 s. The return level estimates for the men’s world record were 9.74, 9.62, and 9.58 s with a 95% confidence interval of [9.69, 9.79], [9.54, 9.69], and [9.48, 9.67] for 10-, 100- and 350-year return periods, respectively. In one year, the probability of occurrence for a new world record of men, 9.58 s (Usain Bolt), was 1/350, while that for women, 10.49 s (Florence Griffith-Joyner), was about 1/100, confirming it was more difficult for men to break records than women.展开更多
Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the human lifespan in the world and Japan. The diagnostic plots, whi...Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the human lifespan in the world and Japan. The diagnostic plots, which assessed the accuracy of the GEV model, were fitted to the human lifespan, validating the model. The human lifespan in the world and Japan had shape parameters of ?0.1623 and ?0.2949 and had an upper limit. The calculated upper limit in the world was 128.7 years. The world’s oldest record holder, Jeanne Calment’s age of 122.45 years, was close to the 260-year return level and was far from the calculated upper limit. The calculated upper limit in Japan was 120.4 years. Japan’s oldest record holder, Kane Tanaka’s age of 119 years in 2022, was the 500-year return level and was close to the upper limit. In the world, achieving the calculated limit was difficult, but the human lifespan will soon reach the upper limit in Japan.展开更多
Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the ultimate 100 m, 200 m, 400 m, 4 × 100 m relay, and long jum...Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the ultimate 100 m, 200 m, 400 m, 4 × 100 m relay, and long jump records of male gold medalists at the Olympics. The diagnostic plots, which assessed the accuracy of the GEV model, were fitted to all event records, validating the model. The 100 m, 200 m, 400 m, 4 × 100 m, and long jump records had negative shape parameters and calculated upper limits of 9.58 s, 19.18 s, 42.97 s, 36.71 s, and 9.03 m, respectively. The calculated upper limit in the 100 m (9.58 s) was equal to the record of Usain Bolt (August 16, 2009). The 100 m and 200 m world records were close to the calculated upper limits, and achieving the calculated limit was difficult. The 400 m and 4 × 100 m relay world records were almost equal to the calculated upper limits and the 500-year return level estimate, and slight improvement was possible in both. At the Tokyo Olympics in August 2021, in the 100 m, 200 m, and 4 × 100 m, in one year the probability of occurrence for a record was about 1/30. In the 400 m and long jump, it was about 1/20. In the 100 m, 200 m, and 4 × 100 m relay, more difficult records show that a fierce battle has taken place.展开更多
以R软件为分析工具,选择GEV(generalized extreme value distribution)模型拟合四川省泸州市2003～2007年期间PM10每月最高日平均浓度数据,采用极大似然法估计模型的3个参数即位置参数、尺度参数、形状参数,利用所得的参数估计值计算得...以R软件为分析工具,选择GEV(generalized extreme value distribution)模型拟合四川省泸州市2003～2007年期间PM10每月最高日平均浓度数据,采用极大似然法估计模型的3个参数即位置参数、尺度参数、形状参数,利用所得的参数估计值计算得出某一标准值(如GB3095—1996)的重现期;进一步利用参数估计值计算轮廓似然函数,估计某一段固定时间间隔的PM10浓度的重现值以及其置信区间。结果表明,GEV模型能很好地拟合泸州市PM10数据,利用轮廓似然函数估计的不同时间间隔的重现值准确度高,统计结果可以为环境主管部门发布污染状况预警信息提供参考。展开更多
文摘Extreme value theory provides methods to analyze the most extreme parts of data. We predicted the ultimate 100 m dash records for men and women for specific periods using the generalized extreme value (GEV) distribution. The various diagnostic plots, which assessed the accuracy of the GEV model, were well fitted to the 100 m records in the world and Japan, validating the model. The men’s world record had a shape parameter of -0.250 with a 95% confidence interval of [-0.391, -0.109]. The 100 m record had a finite limit and a calculated upper limit was 9.46 s. The return level estimates for the men’s world record were 9.74, 9.62, and 9.58 s with a 95% confidence interval of [9.69, 9.79], [9.54, 9.69], and [9.48, 9.67] for 10-, 100- and 350-year return periods, respectively. In one year, the probability of occurrence for a new world record of men, 9.58 s (Usain Bolt), was 1/350, while that for women, 10.49 s (Florence Griffith-Joyner), was about 1/100, confirming it was more difficult for men to break records than women.
文摘Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the human lifespan in the world and Japan. The diagnostic plots, which assessed the accuracy of the GEV model, were fitted to the human lifespan, validating the model. The human lifespan in the world and Japan had shape parameters of ?0.1623 and ?0.2949 and had an upper limit. The calculated upper limit in the world was 128.7 years. The world’s oldest record holder, Jeanne Calment’s age of 122.45 years, was close to the 260-year return level and was far from the calculated upper limit. The calculated upper limit in Japan was 120.4 years. Japan’s oldest record holder, Kane Tanaka’s age of 119 years in 2022, was the 500-year return level and was close to the upper limit. In the world, achieving the calculated limit was difficult, but the human lifespan will soon reach the upper limit in Japan.
文摘Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the ultimate 100 m, 200 m, 400 m, 4 × 100 m relay, and long jump records of male gold medalists at the Olympics. The diagnostic plots, which assessed the accuracy of the GEV model, were fitted to all event records, validating the model. The 100 m, 200 m, 400 m, 4 × 100 m, and long jump records had negative shape parameters and calculated upper limits of 9.58 s, 19.18 s, 42.97 s, 36.71 s, and 9.03 m, respectively. The calculated upper limit in the 100 m (9.58 s) was equal to the record of Usain Bolt (August 16, 2009). The 100 m and 200 m world records were close to the calculated upper limits, and achieving the calculated limit was difficult. The 400 m and 4 × 100 m relay world records were almost equal to the calculated upper limits and the 500-year return level estimate, and slight improvement was possible in both. At the Tokyo Olympics in August 2021, in the 100 m, 200 m, and 4 × 100 m, in one year the probability of occurrence for a record was about 1/30. In the 400 m and long jump, it was about 1/20. In the 100 m, 200 m, and 4 × 100 m relay, more difficult records show that a fierce battle has taken place.
文摘以R软件为分析工具,选择GEV(generalized extreme value distribution)模型拟合四川省泸州市2003～2007年期间PM10每月最高日平均浓度数据,采用极大似然法估计模型的3个参数即位置参数、尺度参数、形状参数,利用所得的参数估计值计算得出某一标准值(如GB3095—1996)的重现期;进一步利用参数估计值计算轮廓似然函数,估计某一段固定时间间隔的PM10浓度的重现值以及其置信区间。结果表明,GEV模型能很好地拟合泸州市PM10数据,利用轮廓似然函数估计的不同时间间隔的重现值准确度高,统计结果可以为环境主管部门发布污染状况预警信息提供参考。
