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The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric.Two particular cases of statistical data are defined.The existence and uniqueness of a nonlinear connection corresponding to these classes is proved.Two Koszul tensors are introduced in accordance with the Riemannian approach.As applications,the authors treat the Finslerian (α,β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.