Two Estimate Methods Of The Binary Joint Distribution Function

In Financial research, most of the financial phenomenon can be seen as a random vari-ables and the relationships between these phenomenon can be expressed by the joint dis-tribution functions of the random variables.But basically all these distribution functions areundiscovered,even its marginal distributions are not easy to get. This paper inspired by manypapers which estimate the conditional density or conditional distribution function. We usedtwo methods to estimate the binary joint distribution function. The first methods used thecopula theory which often appear in Financial Risk Management and marginal functionsto structure the estimator of the joint distribution function. The second way make use ofthe product formula. Firstly we estimate the marginal distribution of a random variable andthe conditional distribution function of one variable given the other one. Then make use ofthese two estimators to structure the estimators of the joint distribution function. We haveproved that the mean square error between the two estimators and the actual joint distribu-tion functions convergence to zero in setting conditions. And comparing the advantages anddisadvantages of the two estimation methods through analogue simulation.This paper in order to avoid a single point causing contingency and error, take the onewhich has the smallest absolute error as the appropriate copula function. When the absoluteerror is same, we take the smaller variance one. At the same time, the distance is not easy toget and this paper compare the error directly. We found that the copula function estimatorerror where the random variables are independence smaller than the dependence situation.The error is inversely proportional to the cumulative probability point. In the fourth chapterwe found that the binary normal,binary Gumbel and binary Clayton copula function are allcan as the structure function of the samples. But the binary normal copula function is better.The error estimated by copula theory smaller than the Bayes formula method with the samebandwidth.