Conditional limiting distribution of beta-independent random vectors
- Hashorva, Enkelejd
DOIAbstract
AbstractThe paper deals with random vectors X in Rd,d≥2, possessing the stochastic representation X=dARV, where R is a positive random radius independent of the random vector V and A∈Rd×d is a non-singular matrix. If V is uniformly distributed on the unit sphere of Rd, then for any integer m<d we have the stochastic representations (V1,…,Vm)=dW(U1,…,Um) and (Vm+1,…,Vd)=d(1−W2)1/2(Um+1,…,Ud), with W≥0, such that W2 is a beta distributed random variable with parameters m/2,(d−m)/2 and (U1,…,Um),(Um+1,…,Ud) are independent uniformly distributed on the unit spheres of Rm and Rd−m, respectively. Assuming a more general stochastic representation for V in this paper we introduce the class of beta-independent random vectors. For this new class we d...
Add to ORKG