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The mean past lifetime provides the expected time elapsed since the failure of a subject given that he/she has
failed before the time of observation. In this paper, we propose the proportional mean past lifetime model
to study the association between the mean past lifetime function and potential regression covariates. In the
presence of left censoring, martingale estimating equations are developed to estimate the model parameters,
and the asymptotic properties of the resulting estimators are studied. To assess the adequacy of the model, a
goodness of fit test is also investigated. The proposed method is evaluated via simulation studies and further
applied to a data set.
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