TY - JOUR

T1 - Distributional assumptions in chance-constrained programming models of stochastic water pollution

AU - Kataria, Mitesh

AU - Elofsson, Katarina

AU - Hasler, Berit

N1 - Funding Information: Acknowledgments 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.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Chance-constrained programming

KW - Cost effectiveness

KW - Log-normal distribution

KW - Truncated normal distribution

KW - Water pollution

U2 - 10.1007/s10666-009-9205-7

DO - 10.1007/s10666-009-9205-7

M3 - Journal article

AN - SCOPUS:77954222014

VL - 15

SP - 273

EP - 281

JO - Environmental Modeling & Assessment

JF - Environmental Modeling & Assessment

SN - 1420-2026

IS - 4

ER -