Simultaneous Gamma Prediction Limits for Ground Water Monitoring Applications

Abstract Common problems in the analysis of environmental monitoring data are nonnormal distributions (i.e., right skewed such as gamma and lognormal) and the presence of moderate to large numbers of nondetects (i.e., data below a detection or quantification limit). When new monitoring measurements are compared to background (e.g., comparison of a new downgradient ground water measurement to a series of background or upgradient ground water monitoring measurements), prediction intervals are often the statistical method of choice. A limitation of the usual application of normal prediction limits in the analysis of environmental data is the assumption of normality, which is often violated by both extreme concentrations (in background) and the presence of censored data (i.e., nondetects). While nonparametric alternatives are available, they often require larger numbers of background samples than are typically available in routine practice. This paper extends the literature on normal and nonparametric simultaneous prediction intervals to the case of the gamma distribution, which can accommodate a wide variety of nonnormal distributions (with skewed right tails) and the presence of nondetects. Gamma prediction limits are excellent candidates for routine application to ground water monitoring networks at waste disposal facilities and/or other relevant environmental monitoring applications. The method is illustrated using example ground water detection monitoring data. The paper includes a series of tables that can be used for routine application of the statistical methodology.