In this thesis, I define and explain the notion of punctual analytical uniform development (DUAP) versus moments or cumulants approximation of punctual uniforms analyticals 's class statistics. Hence, I derive "truncated" DUAP's version for numerical computation and implementation which called finite DUAP (F-DUAP). Using F-DUAP approximation lead to an error which was estimated. Due to nature's one of axiom of UAP statistics, the concept extension of DUAP method, to an other class statistic is limited. So, a new local theoretical concept was defined named analytical uniform development (DUA). This generalization let all derived DUAP's theorems become more general. Automatic differentiation and F-DUAP allow the implementation of DUAP or DUA method's on computer: I write the CUMAD and CUMADG codes that make the methods of a practical use. By, the programme CUMAD, I valid the utility of DUAP method, when I applied it to the approximation to moments of "weighted sum of squares statistic".