Stochastic DEA with Using of Skew-Normal Distribution in Error Structure

Subject Areas : Statistics

A. Nazari ¹ , M-H .Behzadi ²

1 - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran Corresponding author

Received: 2015-05-15 Accepted : 2015-12-16 Published : 2015-03-21

Keywords: تحلیل پوششی داده‌ها, برنامه‌ریزی درجه دوم, توزیع چوله &amp, ndash, نرمال, توزیع چوله &amp, ndash, نرمال بسته,

Abstract :

The stochastic data envelopment analysis (SDEA) was developed considering the value ofinputs and outputs as random variables. Therefore, statistical distributions play an importantrole in this regard. The skew-normal (SN) distribution is a family of probability densityfunctions that is frequently used in practical situations. In this paper, we assume that the inputand output variables are skew-normally distributed. With introducing asymmetric errorstructure for random variables of SN distribution, a stochastic BCC model is provided. Theproposed model includes BCC model assuming a normal distribution of data as well. Finally,the proposed model is used in a numerical example

References:

[1] Azzalini, A. (1985). “A Class of Distribution Which Includes the Normal Ones”. Scandinavia Journal of statistic. 12, 171-178.

[2] Azzalini, A. (2005). “The Skew Normal Distribution and Related Multivariate Families”. Scandinavia Journal of statistics. 32, 159-188.

[3] Banker, R.D., Charnes, A. and Cooper, W.W. (1984). “Some models for estimating technical and scale inefficiency in data envelopment analysis”. Management Science. 39, 1078-1092.

[4] Behzadi, M.H., Mirbolouki, M. (2009). “Symmetric Error Structure in Stochastic DEA”. International Journal of Industrial Mathematics. 4, 335-343.

[5] Charnes, A., Cooper, W.W. and Rhodes, E. (1978). “Measuring the efficiency of decision making units”. European Journal of Operational Research. 2, 429-444.

[6] Cooper, W.W., Deng, H., Huang, Z. and Li, S.X. (2004). “Chance constrained programming approaches to congestion in stochastic data envelopment analysis”. European Journal of Operational Research. 155, 487-591.

[7] Cooper, W.W., Huang, Z. and Li, S.X. (1996a). “Satisficing DEA model under chance constraints”. The Annals of Operational Research. 66, 259-279.

[8] Cooper, W.W., Thompson, R.G. and Thrall, R. (1996b). “Extensions and new development in DEA”. The Annals of Operational Research. 66, 3-46.

[9] Farrell, M. J. (1957), “The Measurement of Productive Efficiency”. Journal of the Royal Statistical Society. Series A (General). 120(3), 253-290.

[10] Hosseinzadeh-Lotfi, F., Nematollahi, N., Behzadi, M.H., Mirbolouki, M. and Moghadas, Z. (2012). “Centralized resource allocation with stochastic data”. Journal of computation and Applied Mathematics. 236, 1783-1788

[11] Huang, Z &, Li, S.X. (2001). “Stochastic DEA model with different types of input-output disturbance”. Journal of Productivity Analysis. 15, 95- 113.

[12] Khodabakhshi, M. (2009). “Estimating most productive scale size with stochastic data in data envelopment analysis”. Economic Modelling. 26, 68- 973.

[13] Khodabakhshi, M., Asgharian, M. (2008). “An input relaxation measure of efficiency in stochastic data envelopment analysis”. Applied Mathematical Modelling. 33, 2010-1023.