This　paper　mainly　contributes　to　a　classification　of　statistical　Einstein　manifolds,　namely　statistical　manifolds　at　the　same　time　are　Einstein　manifolds.　A　statistical　manifold　is　a　Riemannian　manifold,　each　of　whose　points　is　a　probability　distribution.　With　the　Fisher　information　metric　as　a　Riemannian　metric,　information　geometry　was　developed　to　understand　the　intrinsic　properties　of　statistical　models,　which　play　important　roles　in　statistical　inference,　etc.　Among　all　these　models,　exponential　families　is　one　of　the　most　important　kinds,　whose　geometric　structures　are　fully　determined　by　their　potential　functions.　To　classify　statistical　Einstein　manifolds,　we　derive　partial　differential　equations　for　potential　functions　of　exponential　families;　special　solutions　of　these　equations　are　obtained　through　the　ansatz　method　as　well　as　group-invariant　solutions　via　reductions　using　Lie　point　symmetries.　(C)　2019　Elsevier　Inc.　All　rights　reserved.