This paper proposes a general formulation of a nonparametric frontier model introducingexternal environmental factors that might influence the production process butare neither inputs nor outputs under the control of the producer. A representation isproposed in terms of a probabilistic model...

Directional distances provide useful, flexible measures of technical efficiency of production units relative to the efficient frontier of the attainable set in input-output space. In addition, the additive nature of directional distances permits negative input or outputs quantities. The choice...