RT Generic
T1 Characterizations involving conditional expectations based on a functional derivative approach
A1 Lillo Rodríguez, Rosa Elvira
A1 Martín, Miguel
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB We introduce a notion of the derivative with respect to a distribution function, not relating necessarily to probability, which generalizes the concept of the derivative as proposed by Lebesgue (1973). The differential calculus required to solve the linear differential equation involved in this notion of the derivative is included in the paper. The definition given here may also be considered as the inverse operator of a modified notion of the Riemmann--Stieltjes integral. Both this unified approach and the results of differential calculus allow us to characterize distributions in terms of three different types of conditional expectations. In applying these results, a test of goodness-of-fit is also indicated. Finally, two characterizations of a general Poisson process are included, based on conditional expectations. Specifically, a useful result for the homogeneous Poisson process is generalized to a general context.
YR 2000
FD 2000-02
LK https://hdl.handle.net/10016/9864
UL https://hdl.handle.net/10016/9864
LA eng
DS e-Archivo
RD 18 may. 2024