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This book synthesizes the recent developments on analysis of left truncated right censored data, mainly from the point of view of parametric inference. The coverage includes different parametric models, inferential methods based on observed likelihood function, expectation maximization algorithm, Bayesian methods, model selection procedures, and analysis of competing risks data, all within the realm of left truncation and right censoring. It also includes brief discussions on semiparametric models that have been recently used for left truncated right censored data, left truncated interval censored data, and truncated and doubly-censored data. The book presents recent developments on statistical literature in this area in a single volume to advanced postgraduate students, researchers, and practitioners.