Estimating the numbers of prison terms in criminal careers from one-step probabilities of recidivism

A method of using estimates of one-step probabilities of recidivism, i.e., conditional probabilities of individuals returning to prison for the jth time given release for the (j-1)st time, to estimate the numbers of prison terms expected to be accumulated by the individuals, is presented. The method is illustrated by calculating the expected numbers of prison terms separately for racial and gender groups in a large data base of Western Australian prisoners. The recidivism probabilities for these data were estimated by fitting Weibull mixture models to the (possibly censored) times to recidivate. The probabilities increase strongly asj increases from 1 to 6, then level off. Large differences between them are due to racial and gender group and these are reflected in the differing expected prison career durations for these groups. The effect of interventions which might lower recidivism is discussed in the light of the method as applied to these estimates.