Practitioner advice: Approximation of the cumulative density of left-sided truncated normal distribution using logistic function and its implementation in Microsoft Excel

The left-sided truncated normal distribution is especially important in quality engineering where we remove the left side of the distribution, for example, due to estimation of the life of used products. Although the theoretical background of truncated normal distribution is already established, there is very little work on mathematical approximation of the probability density and the cumulative probability density functions. In this article, a high accuracy mathematical approximation of the left-sided truncated normal distribution is proposed. A full analysis of errors and recommendations for implementation using Microsoft Excel are provided at the end of this article.