Abstract: A system is considered in which switching takes place between sub-systems according to a continuous parameter Markov chain. Failures may occur in Poisson processes in the sub-systems, and in the transitions between subsystems. All failure processes are independent. The overall failure process is described exactly and asymptotically for highly reliable sub-systems. An application to process-control computer software is suggested.

Abstract: SUMMARY In the study of the effects of several factors on vital rates, the single-factor specific rates can be misleading if the factors are not independent. Maximum likelihood estimates of the parameters of a multiplicative model are derived and the model is fitted to data of stillbirth rates to estimate the independent effects of maternal age and parity.

Abstract: The paper tabulates the cumulative distribution functions of standardized symmetrical stable laws with exponent α = 0.6 (0.1) 2.0, the standardization being such that the special values α = 1.0, α = 2.0 correspond, without further adjustment, to the standard Cauchy and Normal cases as usually defined. The tables were computed by numerical inversion of the characteristic functions.

Abstract: SUMMARY In recent years, the theory of evolutionary spectral analysis of non-stationary time series has been fairly widely used. However, owing to the difficulty of deriving exact sampling results, all the studies undertaken to date rely mainly on approximate results. In the absence of exact results, it is therefore of interest to conduct a fairly extensive simulation study.