  The thermodynamic properties of the de Rham-Gabadadze-Tolley (dRGT) black
hole in the asymptotically de Sitter (dS) spacetime are investigated by using
R\'enyi entropy. It has been found that the black hole with asymptotically dS
spacetime described by the standard Gibbs-Boltzmann statistics cannot be
thermodynamically stable. Moreover, there generically exist two horizons
corresponding to two thermodynamic systems with different temperatures, leading
to a nonequilibrium state. Therefore, in order to obtain the stable dRGT black
hole, we use the alternative R\'enyi statistics to analyze the thermodynamics
properties in both the separated system approach and the effective system
approach. Interestingly, we found that it is possible concurrently obtain
positive pressure and volume for the dRGT black hole while it is not for the
Schwarzschild-de Sitter (Sch-dS) black hole. Furthermore, the bounds on the
nonextensive parameter for which the black hole being thermodynamically stable
are determined. In addition, the key differences between the systems described
by different approaches, e.g., temperature profiles and types of the
Hawking-Page phase transition are pointed out.
