Computational Statistics

, Volume 33, Issue 2, pp 967–982 | Cite as

Likelihood computation in the normal-gamma stochastic frontier model

  • Bernardo B. de Andrade
  • Geraldo S. Souza
Original Paper


Likelihood-based estimation of the normal-gamma stochastic frontier model requires numerical integration to solve its likelihood. For the integration methods found in the literature, it is not known under which conditions they perform optimally or if there is a method that performs better than the others. Our aim is to study the applicability of available methods and to compare them based on their ability to approximate the loglikelihood. We consider three principles—numerical quadrature, inversion of the characteristic function and Monte Carlo—and assess the effect of the parameters on the accuracy of each of six numerical procedures.


Fourier transform Gaussian quadrature Random effects Randomized quasi-Monte Carlo 



GSS is grateful to the National Council for Scientific and Technological Development—CNPq/Brazil, for financial support. BBA has been partially funded by the Federal District Research Foundation, FAP/DF.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of BrasíliaBrasíliaBrazil
  2. 2.Brazilian Agricultural Research Corporation (EMBRAPA)Parque Estação Biológica, Asa NorteBrasíliaBrazil

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