Approximating the mean of a truncated normal distribution

TL;DR

This paper introduces an iterative deterministic method to approximate the mean of a truncated normal distribution, inspired by MCMC schemes, with proven convergence and demonstrated rapid accuracy through simulations.

Contribution

It presents a novel deterministic iterative scheme for estimating the mean of a truncated normal distribution, extending previous models and providing convergence guarantees.

Findings

The scheme converges to a unique fixed point.

Simulations show rapid convergence to the true mean.

The method is effective for practical applications.

Abstract

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.