We give estimates of the distance between the densities of the laws of two functionals F and G on the Wiener space in terms of the Malliavin-Sobolev norm of F −G. We actually consider a more general framework which allows one to treat with similar (Malliavin type) methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to...

We present an algorithm for grouping families of probability density functions (pdfs). We exploit the fact that under the square-root re-parametrization, the space of pdfs forms a Riemannian manifold, namely the unit Hilbert sphere. An immediate consequence of this re-parametrization is that different families of pdfs form different submanifolds of the unit Hilbert sphere. Therefore, the proble...

Bhat et al. [1] developed an inductive compiler that computes density functions for probability spaces described by programs in a probabilistic functional language. In this work, we implement such a compiler for a modified version of this language within the theorem prover Isabelle and give a formal proof of its soundness w.r.t. the semantics of the source and target language. Together with Isa...

An exact expression is obtained for the probability density function (pdf) of any quantity measured in a general stationary process, in terms of conditional expectations of time derivatives of the signal. This expression indicates that the conditional expectations of both the time derivative squared and of the second time derivative influence the shape of the pdf, including its tails. A previou...

There exist many approaches to discern a functional relationship between two variables. A functional model is useful for two reasons: Firstly, if the function is a relatively simple model in the plane, it provides us with qualitative information about the relationship. Secondly, given a fixed value for one variable, the other one can be calculated as a means for prediction. In this paper an app...

In order to improve the calculation accuracy of rainfall probability distribution in related applications, this study aimed select a theoretical function from applicable functions for three classes class-conditional density (CCPD) hourly series. The are generalized gamma (GΓD), normal (GND), and Weibull distribution. For reason that it is hard distinguish advantages disadvantages by plot error ...