  The NPMLE of a distribution function from doubly truncated data was
introduced in the seminal paper of Efron and Petrosian. The consistency of the
Efron-Petrosian estimator depends however on the assumption of independent
truncation. In this work we introduce an extension of the Efron-Petrosian NPMLE
when the variable of interest and the truncation variables may be dependent.
The proposed estimator is constructed on the basis of a copula function which
represents the dependence structure between the variable of interest and the
truncation variables. Two different iterative algorithms to compute the
estimator in practice are introduced, and their performance is explored through
an intensive Monte Carlo simulation study. We illustrate the use of the
estimators on two real data examples.
