Exponential-Wrapped Distributions on $\text {SL}(2, \mathbb {C})$ and the Möbius Group.

In this paper we discuss the construction of probability distributions on the group \(\text {SL}(2,\mathbb {C})\) and the Mobius group using the exponential map. In particular, we describe the injectivity and surjectivity domains of the exponential map and provide its Jacobian determinant. We also show that on \(\text {SL}(2,\mathbb {C})\) and the Mobius group, there are no isotropic distributions in the group sense.