Some probabilistic properties of B-splines and an application to dimensional tolerance

Abstract

The paper shows that normalized B-splines can be directly utilized as a probability model for representing a wide variety of probability density-function shapes with finite bounds, and it is shown how they can be trivially extended to represent random vectors. It is further shown that normalized Bernstein functions are particular beta functions.

For uniform B-splines, a relationship between the order and the corresponding variance of the B-spline density function is proved.

An application of the B-spline probability model to dimensional tolerances is proposed as an approximation and an alternative distribution.