The Combination Distribution Model And Application

Extreme value theory is an important branch of probability and statistics, is a powerfulweapon of the description of the objective world of extreme risk, are widely used in the fieldof earthquakes, floods, financial securities, project investment, however there is a lot of factsthat, in some extreme cases, a single the distribution can not accurately describe the extremerisk Therefore, the combination of distribution methods came into being but currently seen inthe literature, are more or less there is some problems, and not be able to accurately andappropriately reflect the objective reality paper In response to this situation, summed up andcorrect the error in the previous studies, follow the thinking of predecessors combineddistribution method, to the knowledge of the statistical theory of extreme tools, from astatistical point of view, given a new combination of distribution model to discuss the natureof the distribution model of the new combination, through examples of calculated andcompared with the existing results, the proposed combination of reasonable distributionmodel and superiority.The paper first analyzes the error the combination distribution model predecessors(original combination distribution model): the original model tried by the minimum value ofthe distribution, the original distribution, distribution of maxima three simple distributionfunction at different intervals distribution segment combination of tectonic combination.Unfortunately, its definition of breach of the distribution function nondecreasing In addition,the the original combination distribution model in the handling of the parameter estimationmethod, also there are certain problems for this situation, the paper In the second chapter, thefirst clear structure combined distribution principles, and on this basis, and given a reasonabledemonstration of the definition of the new combined distribution model and newcombinations of distribution models. third chapter is the full text of the work of the center,that the new combined distribution modeling process in this chapter, first given priorknowledge of the combination of the distribution model, the errors in the original combinationdistribution model defined theoretical proof. then focuses on the combination of the distribution model of the detailed steps determine the method of the original distribution andthe tail distribution type and parameter estimation method, the extreme value distributionparameter estimation method. extreme value distribution parameter maximum likelihoodestimation no analytical solution, the paper also highlights the Gumbel distribution parameterestimation method, Gumbel distribution parameters numerical solution maximum likelihoodmethod and procedures through MATLAB Chapter will combine the distribution model isapplied to the area of rainfall, the stock market, and river flow problems, the same sampledata were applied to the front have studied the distribution model and combined distributionmodel, the P value of the KS test for comparing the two instance calculation results show that,in some extreme cases, the combined distribution model as defined herein compared toconventional single distribution, Not only can more accurately describe the extreme risks, itsflexible application methods, the wide range of applications is also unmatched by previousresults.The combination distribution model is a new attempt to portray the extreme risk randomcharacteristics, it can better estimate extreme risk, this is the charm of the combineddistribution.