  In this work, we examine thermalon phase transition between AdS and dS vacua
in Einstein-Gauss-Bonnet gravity by considering the R\'{e}nyi statistics. The
thermalon changes the asymptotic structure of spacetimes via the bubble
nucleation of spherical thin-shells which host a black hole in the interior.
All relevant thermodynamical quantities are computed in terms of the R\'{e}nyi
statistics in order to demonstrate the possible existence of the AdS to dS
phase transition. In addition, we also comment on the behaviors of the phase
transitions in the R\'{e}nyi statistics.
