Maximum likelihood estimation of life-span based on censored and passively registered historical data

We consider the estimation of life length of people who were born in the seventeenth or eighteenth century in England. The data consist of a sequence of times of life events that is either ended by a time of death or is right-censored by an unobserved time of migration. We propose a semi parametric model for the data and use a maximum likelihood method to estimate the unknown parameters in this model. We prove the consistency of the maximum likelihood estimators and describe an algorithm to obtain the estimates numerically. We have applied the algorithm to data and the estimates found are presented.