Detection of frailty in Weibull lifetime data using Outlier tests

Heterogeneity in lifetime data may be modelled by multiplying an individual's hazard by an unobserved frailty. We test for the presence of frailty of this kind in univariate and bivariate data with Weibull distributed lifetimes, using statistics based on the ordered Cox-Snell residuals from the null model of no frailty. The form of the statistics is suggested by outlier testing in the gamma distribution. We find through simulation that the sum of the k largest or k smallest order statistics, for suitably chosen k , provides a powerful test when the frailty distribution is assumed to be gamma or positive stable, respectively. We provide recommended values of k for sample sizes up to 100 and simple formulae for estimated critical values for tests at the 5% level.

Meteorological factors controlling low-level continental pollutant outflow across a coast

Coastal outflow describes the horizontal advection of pollutants from the continental boundary layer across a coastline into a layer above the marine boundary layer. This process can ventilate polluted continental boundary layers and thus regulate air quality in highly populated coastal regions. This paper investigates the factors controlling coastal outflow and quantifies its importance as a ventilation mechanism. Tracers in the Met Office Unified Model (MetUM) are used to examine the magnitude and variability of coastal outflow over the eastern United States for a 4 week period during summer 2004. Over the 4 week period, ventilation of tracer from the continental boundary layer via coastal outflow occurs with the same magnitude as vertical ventilation via convection and advection. The relative importance of tracer decay rate, cross-coastal advection rate, and a parameter based on the relative continental and marine boundary layer heights, on coastal outflow is assessed by reducing the problem to a time-dependent box-model. The ratio of the advection rate and decay rate is a dimensionless parameter which determines whether tracers are long-lived or short-lived. Long- and short-lived tracers exhibit different behaviours with respect to coastal outflow. For short-lived tracers, increasing the advection rate increases the diurnally averaged magnitude of coastal outflow, but has the opposite effect for very long-lived tracers. Short-lived tracers exhibit large diurnal variability in coastal outflow but long-lived tracers do not. By combining the MetUM and box-model simulations a landwidth is determined which represents the distance inland over which emissions contribute significantly to coastal outflow. A landwidth of between 100 and 400 km is found to be representative for a tracer with a lifetime of 24 h.