Approximating the mean of a truncated normal distribution

A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from an iterative Markov chain Monte Carlo (MCMC) scheme that addresses this problem and it can be viewed as a generalization of a recently proposed relevant model. Conditions are provided under which it is proved that the scheme converges to a unique fixed point. Finally, the theoretical results are also supported by computer simulations, which also show the rapid convergence of the method to a solution vector that is very close to the mean of the truncated normal distribution under study.