Roy Saunders

A NOTE ON THE COST OF CARRIER-BORNE, RIGHT-SHIFT, EPIDEMIC MODELS

We establish a sufficient condition for which the expected area under the trajectory of the carrier process is directly proportional to the expected number of removed carriers in the class of carrier-borne, right-shift, epidemic models studied by Severo (1969a). This result generalizes the previous work of Downton (1972) and Jerwood (1974) for some special cases of these models. We use the result to compute expected costs in the carrier-borne model due to Downton (1968) when it is unlikely that all the susceptibles will be infected. We conclude by showing that for the special case considered by Weiss (1965) this treatment of the expected cost is reasonable for populations with a large initial number of susceptibles. CARRIER-BORNE EPIDEMICS; COST; AREA UNDER TRAJECTORY OF CARRIERS; EXPECTED NUMBER OF CARRIER REMOVALS; RIGHT-SHIFT PROCESSES

NORMAL APPROXIMATIONS FOR BINARY LATTICE SYSTEMS

Consider an array of binary random variables distributed over an m,(n) by m2(n) rectangular lattice and let Y,(n) denote the number of pairs of variables d, units apart and both equal to 1. We show that if the binary variables are independent and identically distributed, then under certain conditions Y(n)(Y,(n), - - -, Y,(n)) is asymptotically multivariate normal for n large and r finite. This result is extended to versions of a model which provide clustering (repulsion) alternatives to randomness and have clustering (repulsion) parameter values nearly equal to 0. Statistical applications of these results are discussed.

ON JOINT EXCHANGEABILITY AND CONSERVATIVE PROCESSES WITH STOCHASTIC RATES

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.

A Note on Shock Model Justification for IFR Distributions

We consider the model in which the failure rate for a device changes when the device is subjected to shocks which occur stochastically over time. We show that increasing failure rate distributions can be obtained by making simple models for the effects of shocks. The results provide a physical motivation for using the Weibull distributions for failure time data. Random failure rates used in Bayesian inference are also obtained in a similar manner by modeling the effects of shocks to be stochastic.

A test of independence in the presence of discrete points

This article develops a distribution-free method for testing the independence of two random variables, each of which is continuous except at one discrete point, Two possible generalizations are also discussed briefly.