V. Henschel, W.-D. Richter
Geometric generalization of the exponential law
Preprint series: Preprints aus dem Fachbereich Mathematik
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
Abstract: For the regular simplicial or $\ell_1$-norm symmetric distributions,
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.
Keywords: Exponential and $\ell_1$-norm symmetric distributions, modified t-test, F-distribution