MATHEMATICAL APPROXIMATION OF SINGLE- AND DOUBLE-SIDED TRUNCATED NORMAL DISTRIBUTION USING LOGISTIC FUNCTION

This article provides a mathematical approximation model to the general double-sided truncated normal distribution, as an extension of the case of the left-sided truncated normal distribution modeled by Hamasha (2016). The right- and left-sided cases are included in the model as special cases of the introduced double-sided general model. Then, the double-sided case itself is modeled and analyzed. The double-sided truncated normal distribution is important for many applications in industrial and systems engineering. For example, in quality control, production engineers may be interested in scrapping unfit products. The distribution of product variations after this scrapping is basically a double-sided truncated distribution. A full analysis of the deviation of the introduced approximation's results from the actual results is detailed. Further, recommendations for the use of the model are suggested. The main contribution is to provide industrial practitioners with a strong tool to approximate the normal distribution when it is truncated from any or both sides for any reason.