Estimation of Parameters of the Truncated Normal Distribution with Unknown Bounds

The expectation-maximization (EM) algorithm is a commonly used iterative algorithm for providing parameter estimates of distributions for truncated samples when the truncation points or number of missing observations are known. There is also literature for estimating the unknown bounds of truncated distributions. However, there are no works that accommodate both parameter and bound estimation. In this work, we propose a methodology and an iterative algorithm known as an expectation-solution (ES) algorithm to estimate the location, scale, and truncation parameters of the truncated normal distribution. A preliminary simulation study illustrates the utility of this methodology.