Distributional Assumptions in Chance-Constrained Programming Models of Stochastic Water Pollution
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In the water management literature both the normal and log-normal distribution are commonly used to model stochastic water pollution. The normality assumption is usually motivated by the central limit theorem, while the log-normality assumption is often motivated by the need to avoid the possibility of negative pollution loads. We utilize the truncated normal distribution as an alternative to these distributions. Using probabilistic constraints in a cost-minimization model for the Baltic Sea, we show that the distribution assumption bias is between 1% and 60%. Simulations show that a greater difference is to be expected for data with a higher degree of truncation. Using the normal distribution instead of the truncated normal distribution leads to an underestimation of the true cost. On the contrary, the difference in cost when using the normal versus the log-normal can be positive as well as negative.
KeywordsCost effectiveness Water pollution Chance-constrained programming Log-normal distribution Truncated normal distribution
The authors want to thank Clas Eriksson, Karin Larsen, Monica Campos, Yves Surry, and Erik Ansink for valuable comments. The usual disclaimer applies. Funding from Baltic Nest Institute, Aarhus University, Denmark, and the BONUS program is gratefully acknowledged.
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