Abstract
We prove that an independence property established by Matsumoto and Yor [2001. An analogue of Pitman's 2 M - X theorem for exponential Wiener functional, Part II: the role of the generalized inverse Gaussian laws. Nagoya Math. J. 162, 65–86] and by Letac and Wesolowski [2000. An independence property for the product of GIG and gamma laws. Ann. Probab. 28, 1371–1383] is, in a particular case, a corollary of a result by Barndorff-Nielsen and Koudou [1998. Trees with random conductivities and the (reciprocal) inverse Gaussian distribution. Adv. Appl. Probab. 30, 409–424] where, for finite trees equipped with inverse Gaussian resistances, an exact distributional and independence result was established.
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