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Abstract:
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LN distributions are often assumed for environmental contaminants, with some justification. But decisions are made from measurements, not unobservable concentrations. These are not LN in general; rather, at fixed concentrations distributions of measurements are often normal, and if low-level measurements are unbiased one has negative values. The mixture model presented has five physically meaningful parameters. This reality is universally ignored; rather, values are censored at a Reporting Limit, negative values are never seen, and we continue to develop methods for left-censored LN environmental data. The inference in the motivating application involves Upper Tolerance Limits in Industrial Hygiene. We show that censored-data LN methods provide conservative UTLs that become more conservative as the RL decreases and suggest better approaches using uncensored data.
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