EM Algorithm for Parameter Estimation Under Censoring Schemes

Performs parameter estimation using the Expectation-Maximization (EM) algorithm of Dempster, Laird, and Rubin (1977) for arbitrary univariate probability distributions under numerous censoring and truncation schemes. Users supply the probability density function (PDF), cumulative distribution function (CDF), survival function, initial parameter vector, support bounds, and observed data; the package automatically estimates parameters using the EM algorithm under the specified censoring scheme. Supported schemes include complete data, right censoring, left censoring, interval censoring, random censoring, block random censoring, Type-I censoring, Type-II censoring, progressive Type-II censoring (Balakrishnan and Aggarwala (2000, ISBN:978-1-4612-1334-5)), progressive first failure censoring, joint Type-I censoring, joint Type-II censoring, balanced joint progressive Type-II censoring, hybrid censoring, hybrid Type-I censoring, hybrid Type-II censoring, Type-I hybrid censoring, Type-II progressively hybrid censoring, doubly Type-II censoring, middle censoring, right truncation, and left truncation. Standard errors are computed via the observed information matrix (numerical Hessian), the Louis (1982) method, and the supplemented EM (SEM) algorithm of Meng and Rubin (1991) . The package also provides confidence intervals, model selection criteria (AIC, BIC, AICc, HQIC), goodness-of-fit statistics (Kolmogorov-Smirnov, Cramer-von Mises, Anderson-Darling), residual analysis (randomized quantile residuals, generalized residuals), parametric bootstrap methods, Aitken acceleration for convergence improvement, and comprehensive visualization tools. References: Wu and Kus (2009) , Kundu and Joarder (2006) , Iyer, Jammalamadaka, and Kundu (2008) , Banerjee and Kundu (2008) , Prajapati, Mitra, and Kundu (2019) , Mondal and Kundu (2020) , Ding and Gui (2023) .