The Method Of Construct Distribution Function By Spline Function And Its Application

The thesis is composed of five chapters.The first chapter put forwards the study object is distribution function, and introduces the different arithmetics of distribution function by others. Based on these, using theory of B-spline function, the anthor puts forward a new algorithm of distribution function. The second chapter gives the necessary foundation knowledge of this arithmetic.The next two chapters are the main content. From empirical distribution function, using theory of spline function , give new algorithms of monad distribution function and multivariate distribution function separately. First, the anthor gives a new algorithm of monad distribution function. Under given level, this distribution function can pass Kolmogorov criterion, thus it can approximate sample's real distribution function. Then, the anthor extends the definition of empirical distribution function to generalized function. Cites duality function as an example, supposed the sample's real distribution function exists, using bicubic B-spline function, gives a new algorithm of duality distribution function. In real calculation, what we should do is just using empirical distribution function to replace real distribution function. Therefore, to subsample's observation of continuous random sample parent population, if we can't get its material function easily, or we don't know its density function, we can use this way to approximate its distribution function. And these methods can achieve good approximation effect.The fifth chapter summarizes the whole thesis and bring forward some place which need to be improved.