**MSC:**- 60D05 Geometric probability, stochastic geometry, random sets, See also {52A22, 53C65}
- 60E05 Distributions: general theory
- 62E15 Exact distribution theory
- 62F04 Small sample properties of tests
- 62F25 Tolerance and confidence regions

which are generalizations of the $n$-dimensional exponential

distribution with independent marginals, a geometric representation

formula together with some of its basic properties is given. This

formula can especially fruitfully be applied to a new developed and

statistically well motivated system of sets. From that the

distribution of a $t$-statistic adapted for the two parametric

exponential distribution is got, significance tests and confidence

intervals are derived, and classes of F-distributed random variables

are deduced.