In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common h...In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.展开更多
Short-duration heavy rainfall（SDHR） is a type of severe convective weather that often leads to substantial losses of property and life. We derive the spatiotemporal distribution and diurnal variation of SDHR over Ch...Short-duration heavy rainfall（SDHR） is a type of severe convective weather that often leads to substantial losses of property and life. We derive the spatiotemporal distribution and diurnal variation of SDHR over China during the warm season（April–September） from quality-controlled hourly raingauge data taken at 876 stations for 19 yr（1991–2009）, in comparison with the diurnal features of the mesoscale convective systems（MCSs） derived from satellite data. The results are as follows. 1） Spatial distributions of the frequency of SDHR events with hourly rainfall greater than 10–40 mm are very similar to the distribution of heavy rainfall（daily rainfall 50 mm） over China's Mainland. 2） SDHR occurs most frequently in South China such as southern Yunnan, Guizhou, and Jiangxi provinces, the Sichuan basin, and the lower reaches of the Yangtze River, among others. Some SDHR events with hourly rainfall 50 mm also occur in northern China, e.g., the western Xinjiang and central-eastern Inner Mongolia. The heaviest hourly rainfall is observed over the Hainan Island with the amount reaching over 180 mm. 3） The frequency of the SDHR events is the highest in July, followed by August. Analysis of pentad variations in SDHR reveals that SDHR events are intermittent, with the fourth pentad of July the most active. The frequency of SDHR over China's Mainland increases slowly with the advent of the East Asian summer monsoon, but decreases rapidly with its withdrawal. 4） The diurnal peak of the SDHR activity occurs in the later afternoon（1600–1700 Beijing Time（BT））, and the secondary peak occurs after midnight（0100–0200 BT） and in the early morning（0700–0800 BT）; whereas the diurnal minimum occurs around late morning till noon（1000–1300 BT）. 5） The diurnal variation of SDHR exhibits generally consistent features with that of the MCSs in China, but the active periods and propagation of SDHR and MCSs difer in diferent regions. The number and duration of local maxima in the d展开更多
Experimental researches were conducted on flood carrying capacity of compound open channels with wide and narrow floodplains as well as hydrodynamic behavior of overbank flow across vegetated floodplains. Results show...Experimental researches were conducted on flood carrying capacity of compound open channels with wide and narrow floodplains as well as hydrodynamic behavior of overbank flow across vegetated floodplains. Results show that hydrodynamic behavior of compound channels with narrow floodplains is different from that of the wide floodplains. In such compound channels with narrow vegetated floodplains as in the Pearl River delta nework, it has been found that vegetated domains become really impenetra ble when the length of vegetated domain is larger than Lm, the length of f low in floodplain coming into the main channel, and that the influence of vegeta ted floodplains upon flood stages of a channel is not very significant.展开更多
In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distrib...In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given.The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081) .
文摘In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
基金Supported by the China Meteorological Administration Special Public Welfare Research Fund (GYHY201206004,GYHY201206003,and GYHY200906003)National (Key) Basic Research and Development (973) Program of China (2013CB430106)
文摘Short-duration heavy rainfall（SDHR） is a type of severe convective weather that often leads to substantial losses of property and life. We derive the spatiotemporal distribution and diurnal variation of SDHR over China during the warm season（April–September） from quality-controlled hourly raingauge data taken at 876 stations for 19 yr（1991–2009）, in comparison with the diurnal features of the mesoscale convective systems（MCSs） derived from satellite data. The results are as follows. 1） Spatial distributions of the frequency of SDHR events with hourly rainfall greater than 10–40 mm are very similar to the distribution of heavy rainfall（daily rainfall 50 mm） over China's Mainland. 2） SDHR occurs most frequently in South China such as southern Yunnan, Guizhou, and Jiangxi provinces, the Sichuan basin, and the lower reaches of the Yangtze River, among others. Some SDHR events with hourly rainfall 50 mm also occur in northern China, e.g., the western Xinjiang and central-eastern Inner Mongolia. The heaviest hourly rainfall is observed over the Hainan Island with the amount reaching over 180 mm. 3） The frequency of the SDHR events is the highest in July, followed by August. Analysis of pentad variations in SDHR reveals that SDHR events are intermittent, with the fourth pentad of July the most active. The frequency of SDHR over China's Mainland increases slowly with the advent of the East Asian summer monsoon, but decreases rapidly with its withdrawal. 4） The diurnal peak of the SDHR activity occurs in the later afternoon（1600–1700 Beijing Time（BT））, and the secondary peak occurs after midnight（0100–0200 BT） and in the early morning（0700–0800 BT）; whereas the diurnal minimum occurs around late morning till noon（1000–1300 BT）. 5） The diurnal variation of SDHR exhibits generally consistent features with that of the MCSs in China, but the active periods and propagation of SDHR and MCSs difer in diferent regions. The number and duration of local maxima in the d
文摘Experimental researches were conducted on flood carrying capacity of compound open channels with wide and narrow floodplains as well as hydrodynamic behavior of overbank flow across vegetated floodplains. Results show that hydrodynamic behavior of compound channels with narrow floodplains is different from that of the wide floodplains. In such compound channels with narrow vegetated floodplains as in the Pearl River delta nework, it has been found that vegetated domains become really impenetra ble when the length of vegetated domain is larger than Lm, the length of f low in floodplain coming into the main channel, and that the influence of vegeta ted floodplains upon flood stages of a channel is not very significant.
基金supported by the National Natural Science Foundation of China(Grant Nos.10271013,10071090).
文摘In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given.The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.
