几种常见概率分布间的关系

书[1]详细讨论了指数分布、X^2分布各自的性质，习题中也提到了Г分布，本文拟讨论这三种分布间的关系，并基此得出一些有用的结论．

A study on the temporal and spatial characteristics of droughts following earthquakes

According to the ＂jacking-up＂ theory, which relates the cause of earthquakes to outer core convection ascension bodies, the crust will gradually recover after an earthquake. In such cases, the crust is stretched, the underground temperature is reduced, precipitation decreases, and drought occurs. In this paper, precipitation is compared with ground temperature and seismic data to determine the spatial and temporal relationship between earthquakes and subsequent droughts. Our objective is to develop a new method of drought prediction. With a few exceptions in location, the analysis of the first drought to occur after the Ms 〉 7 earthquakes in China's Mainland and the adjacent areas since 1950 shows that droughts tended to occur in regions near earthquake epicenters and in the eastern regions of the epicenters at the same latitude within six months after the earthquakes. In addition, and the differences between the starting time of the earthquakes and the droughts nearly share the same probability of 0 to 6 months. After careful analysis of 34 Ms 〉 6.5 earthquakes occurring in western China from 1980 to 2011, we determined that a second drought tends to occur approximately six months following the first drought, indicating a quasi-half-year period. Moreover, the duration of the quasi-half-year fluctuation increases with the magnitude of earthquake, at approximately 2.5 years for Ms 6.5 earthquake and approximately 5 years for Ms 8 earthquake.

Distributional Relations on Impulse Radiating Surface and Point Type Sources

The electromagnetic field relations are demonstrated on impulse radiating surface and point type sources, which are characterized by first and second order singularities at rest in a Schwartz-Sobolev space setting. The investigation starts with a general introduction to Schwartz-Sobolev distributions, the electromagnetic field equations and various modes of impulsive radiation. This is followed by an outline of temporal distributional relations in arbitrary media and distributional derivative operations on an arbitrary regular surface, all of which are employed in an investigation of impulse radiation mechanism on single and double layer sources. Similar steps are followed in a description of point distributions and investigation of impulse radiation mechanism on electric and magnetic point dipoles.

Correlation Analysis of Gridding of Earthquakes in Datong and Its Surrounding Areas and Implication for Earthquake Prediction

On the basis of the earthquake （gL I〉3.0） catalog in North China from 1970 to 2009, the pattern of temporal and spatial distribution of medium-small earthquakes in Datong and its surrounding areas is studied by correlation analysis with a focus on its anomaly before moderate and strong earthquakes. With different spatial scales, temporal scales and time steps, the spatial distribution of earthquakes is converted to a sequence, then the correlation coefficients between the spatial distribution of medium-small earthquakes in a long-term and a longer time are calculated for the analysis of anomalies before moderate and strong earthquakes. In the study region center on the epicenter of the 1989 Datong- Yanggao earthquake （Ms5. 9） within a radius of less than 0.8~, with the time length of 3600 days, the longer time length of 3700 days, and the time step of 100 days, the correlation coefficient from 1980 to 2009 is steady between 0.94 and 1.00, but there were anomalies with values less than 0. 94 in the 2 years before the 1989 Datong-Yanggao earthquake （Ms 5.9）, the 1991 Datong earthquake （ Ms 5.8） and 1999 Hunyuan earthquake （Ms 5. 6 ）, which indicates the spatial distribution of a medium-small earthquake is very different from steady background seismicity. The implication for earthquake prediction from the anomaly of the correlation coefficient is also discussed with the three conclusions： （1） Before moderate and strong earthquakes in Datong and its surrounding areas, the obvious change of spatial distribution patterns of medium-small earthquake can be a kind of seismic precursor of the 2-year time scale for the prediction of an earthquake＇s time. （2） As the study region is restricted within a radius of less than 0. 8~, the result of correlation analysis is also good for the prediction of an earthquake＇s location. （3） The method of correlation analysis in this paper helps recognize the anomaly of spatial distribution of medium-small earthquake.

Using Weights of Evidence in the Spatial Relation Between Infected Snails and Geographic Factors

Schistosomiasis is a serious public health problem in the middle-lower Yangtze River Basin in China. Study of spatial variation of snail distribution that is related to microgeographic factors can help to choose pertinent measures for snail extinguishment and environment rebuilding. This paper studied the theoretical architecture of weights-of-evidence approach. The case study was made for spatial relation between the occurrence of infected snails and geographic factor combinations in Waijiazhou marshland of Poyang Lake region in China. The multievidence data came from the geographical factor combinations by crossing operation of vegetation coverage grade layer, cattle route distance grade layer, and special environment layer (181 combinations in total) in GIS. The calculation of weight contrast index shows that high vegetation coverage, cattle route distance of <45 meters, and special geographic factor "ground depression" had direct spatial relation with the occurrence of infected snails. The verification by crossing operation in GIS indicated 72.45% of the infected snails concentrated on the areas of positive weight contrast index (sequenced in an order of weight contrast index from high to low), demonstrating the high efficiency of the model established in finding infected snails according to the geographic factor combinations that can be explicitly discerned in the study area.

Approximation for counts of head runs

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.