A nonparametrie maximum likelihood estimator for incomplete renewal data

The problem of estimating the lifetime distribution based on data from independently and identically distributed stationary renewal processes is addressed. The data are incomplete. A nonparametric maximum likelihood estimate of the Lifetime distribution is derived using the em algorithm. The missing information principle is used to estimate the standard error of the estimated distribution. The methodology is applied to a problem in the nursing profession where nurses withdraw from active service for a period of time before returning to take up post at a later date. It is important that nurse manpower planners accurately predict this pattern of return. The data analysed are from the Northern Ireland nursing profession.