Adopting Tolerance Regions in Environmental Economics

Main Article Content

Christos P. Kitsos
Thomas L. Toulias


Uncertainty often lies when there is limited knowledge about the process one has to follow regarding the investigation of a real-world problem. In practice, uncertainty is related with the assumed estimation model of the physical problem, and mainly concerns the involved parameters. A typical example
can be an Environmental Economics system. There are many model specifications that estimate the so-called Benefit Area of such system. For the evaluation of the optimal level of pollution, we can adopt the corresponding tolerance region, and hence we can refer to this optimal level via future observations rather than some parameters estimation. Tolerance regions can be either classical or expected tolerance regions. The associated (four) Benefit Areas can be evaluated through a proposed tolerance region procedure, and not through the usual confidence interval/region approach. Therefore, four possible optimal levels of pollution can be obtained, as well as the corresponding tolerance region for the reduction pollution point.

Confidence interval/region, tolerance region, environmental economics, general linear model.

Article Details

How to Cite
Kitsos, C. P., & Toulias, T. L. (2020). Adopting Tolerance Regions in Environmental Economics. Journal of Advances in Mathematics and Computer Science, 34(6), 1-12.
Original Research Article


Kitsos CP, Toulias TL. Hellinger distance between generalized normal distributions. British Journal of Mathematics and Computer Science. 2017;21(2):1-16.

Toulias TL, Kitsos CP. Entropy and information extensions through the generalized normal distribution. In: Bozeman JR et al. (Eds). Stochastic and Data Analysis Methods and Applications in Statistics and Demography. ISAST. 2016;141-156.

Toulias TL. Entropy and information measures for the generalized normal distribution. In: Filus L et al. (Eds). Stochastic Modeling, Data Analysis & Statistical Applications. ISAST. 2015;3-20.

Halkos G, Kitsos CP. Optimal pollution level: a theoretical identification. Applied Economics. 2005;37(2):1475-1483.

Halkos G, Kitsos CP. Mathematics vs. statistics in tackling environmental economics uncertainty. MRBA. 2018;85280.

Pan-American Health Organization. Gender and natural disasters: women, health and development program. Fact Sheet of the Program on Women, Health and Development.
Washington; 1998.

Mitchell T, Tanner T, Lussier K. We know what we need: South Asian women speak out in climate change application. Action Aid International, Johannesburg, London; 2007.

Halkos G, Kitsos CP. Uncertainty in environment economics: the problem of entropy and model choice. Economic Analysis and Policy. 2018;60:127-140.

Wilks S. Determination of sample sizes for setting tolerance limits. Ann of Mat Stat. 1941;12:91-96.

Halkos G, Kitsou D. Uncertainty in optimal pollution levels modelling and evaluating the benefit area. Journal of Environmental Planning and Management. 2018;55(4):678-700.

Kitsou D. Estimating Damage and Abatement Cost Functions to Define Appropriate Environmental Policies. PhD thesis, Univ. of Thessaly; Volos, Greece; 2015.

Halkos G, Kitsos CP. Relative risk and innovation activities: the case of Greece. Innovation Management, Policy & Practice. 2012;14(1):156-159.

Graybill AF. Theory and Applications of the Linear Model. Duxbury Press, Massachussets; 1976.

Halkos G. Economy and Environment (in Greek). Liberal Books Publ., Athens, Greece; 2013.

Halkos G. Optimal abatement of sulphure missions in Europe. Environmental & Resource Economics. 1994;4(2):127-150.

Newbery D. Acid rain. Economic Policy. 1990;11:288-346.

Newbery D. The impact of EC environmental policy on British coal. Oxford Review of Economic Policy. 1993;9(4):66-95.

Mäller KG. International environmental problems. Oxford Review of Economic Policy. 1990;11:80-Wilks S. Mathematical Statistics. John Wiley, New York; 1962.

Kendall MG, Stuart A. The Advanced Theory of Statistics. C. Griffin Ltd, London, UK. 1968;2.

Guttman I. Construction of β-content tolerance regions at confidence level γ for large samples for k-variate normal distribution. Ann Met Stat. 1970;41:376-400.

Muller CH, Kitsos CP Optimal design criteria based on tolerance regions. In: di Bucchianno A etal. (Eds.) Advances in Model-Oriented Design and Analysis (MODA7). 2004;107-115.

Zarikas V, Kitsos CP. Risk analysis with reference class forecasting adopting tolerance regions. In: Kitsos CP et al. (Eds.) Theory and Practice of Risk Assessment. Springer. 2015;235-247.

Fraser D, Haq MS. Structural probability and prediction for the multivariate model. J Royal Stat Soc B.1969;31:317-332.

Ellerton RRW, Kitsos CP, Rinco S. Choosing the optimal order of a response polynomial-structural approach with minimax criterion. Comm Stat Theory and Methods. 1986;15(1):129-136.

Schervish IM. Theory of statistics. Springer Series in Statistics, Springer; 1995.

Kitsos CP, Toulias TL. Confidence and tolerance regions for the signal process. Recent Patents on Signal Processing. 2012;2(2):149-155.

Halkos G. Econometrics: Theory and practice: Instructions in using Eviews, Minitab, SPSS and Excel. Gutenberg, Athens, Greece; 2011.