Rosenblatt's transformation has been used extensively for evaluation of model goodness-of-fit, but it only applies to models whose joint distribution is continuous. In this paper we generalize the transformation so that it applies to arbitrary probability models. The transformation is simple, but has a wide range of possible applications, providing a tool for exploratory data analysis and forma...

Uncertainty parameters in risk assessment can be modeled by different ways viz. probability distribution, possibility distribution, belief measure, depending upon the nature and availability of the data. Different transformations exist for converting expression of one form of uncertainty to another form. In this paper, we reviewed the consistency principles as given by different researchers. Th...

The CPIT transformations do not, in general, give the same set of transformed values for different orderings of the observations in a sample. When these transformations are followed by a test of uniformity to give an overall goodness-of-fit test, it is possible to obtain different results for different orderings of a sample. We consider here the probability that two goodness-of-fit tests based ...

Abstract It is shown that for any given multi-dimensional probability distribution with regularity conditions, there exists a unique coordinate-wise transformation such the transformed satisfies Stein-type identity. A sufficient condition existence referred to as copositivity of distributions. The proof based on an energy minimization problem over totally geodesic subset Wasserstein space. resu...

Dempster−Shafer belief function theory can address a wider class of uncertainty than the standard probability theory does, and this fact appeals the researchers in operations research society for potential application areas. However, the lack of a decision theory of belief functions gives rise to the need to use the probability transformation methods for decision making. For representation of s...