Application Of Ma Xiufeng's Runs Theory To Drought Analysis

Runs occurrence seems to the cyclical phenomenon.Runs theory is mainly applied to reveal the statistical regularities of random events,and quantificationally determine the probability distribution and return period for occurrence duration.Based on runs theory proposed by Ma Xiufeng,this paper introduced the progress of runs theory in mathematics and drought research,and derived the probability calculation formula of runs length and runs number for coin-tossing test,rolling dice test and gambling test.The validity of probability calculation formula with respect to runs length of gambling test was verified using dichotomous test.And we also explored the influence of original probability distribution on runs length statistic characteristics of independent and dependent sequences respectively to obtain the calculation method of runs length and runs number for dependent sequences.Monthly precipitation data series of 37 stations in Guanzhong area of Shaanxi were used to verify the theory in order to reveal the variation characteristics,probability distribution,and return period of drought event.The results of this research could provide scientific guidance for managers with respect to disaster prevention,project planning and so on in study region.The main conclusions are as follows:(1)Occurrence frequency of runs length for coin-tossing test,rolling dice test and gambling test all meet linear difference equation,so the formula of probability and return period of runs length can be derived(2)Statistical property of runs length corresponding to dichotomous test are very close to gambling test if the number of samples is enough.Therefore,the probability problems of runs length can be settled using gambling test.(3)Runs statistics of dependent sequences could be affected by original probability distribution,but runs statistics of independent sequences could not.Parameter-transfer method can be used to calculate the probability characteristic of runs length for dependent sequences.(4)This paper deduced grouping sample number,probability density,probability distribution,expected value and variance expressions of runs number for coin-tossing test and gambling test.The formula of runs number for independent sequences is not capable of calculation of runs number for dependent sequences,so we employ parameter-transfer to calculate the probability characteristic of runs number for dependent sequences.(5)Drought frequency showed a decreased trend with the increase of drought duration at all stations in Guanzhong area.With the same drought duration(l?3),drought frequency showed a decreased trend with the reduction of truncation level.(6)Ma Xiufeng's runs theory is reasonable to describe probability distribution of drought occurrences at low truncation level in Guanzhong area.This indicated that Ma Xiufeng's runs theory is a feasible method for drought analysis.(7)Return period of drought duration increased significantly with the increase of drought duration at all stations in Guanzhong area at truncation level of-0.3.The drought return period was smallest at Huayin station,and it was largest at Yijun station.