Multivariate mixtures of Erlangs for density estimation under censoring

Area of Science:

• Statistics
• Probability Theory
• Computational Statistics

Background:

• Multivariate mixtures of Erlang distributions offer a flexible and analytically tractable approach for density estimation.
• Existing methods for fitting these mixtures can be computationally intensive and may not handle censored or truncated data effectively.

Purpose of the Study:

• To develop a computationally efficient and flexible fitting procedure for multivariate mixtures of Erlang distributions.
• To extend the Expectation-Maximization (EM) algorithm to accommodate randomly censored and fixed truncated data within this mixture model.

Main Methods:

• Iterative application of the Expectation-Maximization (EM) algorithm.
• Introduction of an efficient initialization and adjustment strategy for shape parameter vectors.
• Extension of the EM algorithm to handle censored and truncated data.

Main Results:

• A flexible and effective fitting procedure for multivariate mixtures of Erlangs was developed.
• The proposed algorithm demonstrates computational efficiency.
• The extended EM algorithm successfully handles randomly censored and fixed truncated data.

Conclusions:

• The developed fitting procedure provides an effective and efficient method for multivariate density estimation using Erlang mixtures.
• The algorithm's ability to handle censored and truncated data broadens its applicability in statistical modeling.
• The method's effectiveness is validated through simulations and real-world data analysis.