Mean Residual Lifetime Frailty Models: A Weighted Perspective

The mean residual life frailty model and a subsequent weighted multiplicative mean residual life model that requires weighted multiplicative mean residual lives are considered. The expression and the shape of a mean residual life for some semiparametric models and also for a multiplicative degradation model are given in separate examples. The frailty model represents the lifetime of the population in which the random parameter combines the effects of the subpopulations. We show that for some regular dependencies of the population lifetime on the random parameter, some aging properties of the subpopulations’ lifetimes are preserved for the population lifetime. We indicate that the weighted multiplicative mean residual life model generates positive dependencies of this type. The copula function associated with the model is also derived. Necessary and sufficient conditions for certain aging properties of population lifetimes in the model are determined. Preservation of stochastic orders of two random parameters for the resulting population lifetimes in the model is acquired.

Changes in future precipitation mean and variability across scales

Changes in precipitation variability can have large societal consequences, whether at the short timescales of flash floods or the longer timescales of multi-year droughts. Recent studies have suggested that in future climate projections, precipitation variability rises more steeply than does its mean, leading to concerns about societal impacts. This work evaluates changes in mean precipitation over a broad range of spatial and temporal scales using a range of models from high-resolution regional simulations to millennial-scale global simulations. Results show that changes depend on the scale of aggregation and involve strong regional differences. On local scales that resolve individual rainfall events (hours and tens of kilometers), changes in precipitation distributions are complex and variances rise substantially more than means, as is required given the well-known disproportionate rise in precipitation intensity. On scales that aggregate across many events, distributional changes become simpler and variability changes smaller. At regional scale, future precipitation distributions can be largely reproduced by a simple transformation of present-day precipitation involving a multiplicative shift and a small additive term. The “extra” broadening is negatively correlated with changes in mean precipitation: in strongly “wetting” areas, distributions broaden less than expected from a simple multiplicative mean change; in “drying” areas, distributions narrow less. Precipitation variability changes are therefore of especial concern in the subtropics, which tend to dry under climate change. Outside the tropics, variability changes are similar on timescales from days to decades, i.e. show little frequency dependence. This behavior is highly robust across models, suggesting it may stem from some fundamental constraint.

Effect of concurrent infection with Ostertagia circumcincta and Trichostrongylus colubriformis on the performance of growing lambs consuming fresh herbage

SummaryNinety 4-month-old wether lambs were allocated to an initial slaughter group (n =10) or to one cell (n= 5) of a 4 × 4 factorial treatment design involving four levels of infection with Ostertagia circumcincta (0, 1000, 2000 and 4000 larvae/day) and Trichostrongyluscolubriformis (0, 1000, 2000 and 3000 larvae/day). They were maintained indoors in individual pens and offered freshly cut ryegrass-white clover herbage during an 84-day period of infection after which they were slaughtered. Body protein, fat, water, Ca and P contents were determined. Feed digestibility was determined in all sheep during 5-day periods during weeks 2, 5, 8 and 11. Faecal egg counts were determined and blood samples obtained at intervals and total worm counts done at slaughter.The effects of mixed infection on feed intake and body-weight gain were multiplicative. Mean D.M. intake of sheep infected simply with 3000 larvae of T. colubriformis or with 4000 larvae of O. circtimcincta was reduced by 10 and 8% respectively, but in those infected simultaneously intake was reduced by 30%. Energy retention was depressed mainly by reduction in gross efficiency of use of metabolizable energy in infections with T. colubriformisand by reduction in feed intake in infections with O. circumcincta. The additional effect of mixed infection occurred mainly through further depression in feed intake.There was no interaction between infections in effect on deposition of Ca or P in the body, both species having significant effect. Infection with T. colubriformis caused hypophosphataemia and hypocalcaemia, but infection with O. circumcincta had no effect.The number of worms established by the infections was generally low compared with previous studies with conserved and concentrate feeds. This was associated with relatively low pathogenicity in infection with O. circumcincta and normal pathogenicity with T. colubriformis.Infection with T. colubriformis reduced the number of adult worms of O. circumcincta present at slaughter.