  Prasad and Takloo-Bighash proposed a conjecture which predicts a necessary
condition in terms of epsilon factors for representations of $\mathrm{GL}_n(F)$
and its inner forms to have linear periods. In this rather expository article,
we reformulate their conjecture in the following form: The distinguished
members in each generic $L$-packet $\Pi_\phi$ are determined by the characters
of the component group $S_\phi$ and local epsilon factors. We follow Aubert et
al.\,for the definitions of the $L$-packets and the component groups.
  We observe that under some hypotheses, the reformulated conjecture follows
from the conjectural multiplicity formula recently proposed by Chen Wan for
general spherical varieties and the conjectural integral formula for epsilon
factors which we propose in this article.
