Metrization of statistical divergences is valuable in both theoretical and practical aspects. One approach to obtaining metrics associated with divergences is to consider their fractional powers. Motivated by this idea, Os\'an, Bussandri, and Lamberti (2018) studied the metrization of fractional powers of the Jensen-Shannon divergence between multinomial distributions and posed an open problem. In this short note, we provide an affirmative answer to their conjecture. Moreover, our method is also applicable to fractional powers of $f$-divergences between Cauchy distributions.

翻译：统计散度的可度量化在理论和实践层面均具有重要价值。获得与散度相关联的度量方法之一，是考虑其分数次幂。受此思想启发，Osán、Bussandri与Lamberti（2018）研究了多项分布间Jensen-Shannon散度分数次幂的可度量化问题，并提出一个开放性问题。本短注中，我们对其猜想给出了肯定性证明。此外，我们的方法同样适用于柯西分布间$f$-散度的分数次幂。