‎Local and global cross-sections in probability

‎Department of Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan‎, ‎Iran‎ ‎Abstract‎: ‎In this paper we survey applications of cross-sections in probability models‎. ‎We will calculate the density of maximal invariant by using cross-sections‎. ‎Finally we confirm the inde‎- ‎pendence of the invariant and equivariant parts in the orbital decomposition‎. ‎This conclusion is similar to independence between a complete sufficient statistic and any ancillary statistic‎, ‎which the completeness assumption has been replaced by the invariance assumptions in our conclusion‎.‎