A Stochastic Differential Equation for Exposure Yields a Beta Distribution

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Abstract

This paper presents a stochastic differential equation for exposure based on a modified version of the standard dilution ventilation equation. An equilibrium solution is obtained with the assumption that variability in the rate of change of concentration is proportional to the product of concentration and one minus concentration. Appropriate definitions for concentration are used to ensure a physically consistent model. The probability distribution for exposure that results is the standard beta distribution. This model is supported by several exposure data sets, which fit the beta distribution well. Issues regarding parameter estimation for the beta distribution, and application of the model are presented. Recommendations are made for simultaneously collecting contaminant generation rate information, ventilation rates, and time-dependent breathing-zone tracer concentrations, in addition to the exposure data.

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