Standard tables of truncated standard normal distribution using a new summarizing method

Abstract

Purpose The single- and double-sided truncated normal distributions have been used in a wide range of engineering fields. However, most of the previous research works have focused primarily on the non-truncated population distributions. The authors present reference tables to estimate the values of density and cumulative density functions of truncated normal distribution for practitioners. Finally, the authors explain how to use the tables to estimate other properties, such as mean, median and variance. The purpose of this paper is to provide an efficient method to summarize tables, and furthermore, to provide readers with statistical tables on truncated standard normal distribution. Design/methodology/approach A new methodology is developed to summarize the tables with ordered values. The introduced method allows for the reduction of the number of pages required for such tables into a reasonable level by using linear interpolation. Moreover, it allows for the estimation of the required truncation values accurately with an error value less than 0.005. Findings The data in the tables can be summarized into a significantly reduced amount. The new summarized table can be designed for any number of pages and/or level of error wanted. However, with reducing the level of error, the number of pages increases and vice versa. Originality/value The value of this work is through two major points. First, all provided summarized tables in the literature are for single-sided and symmetry truncation cases. However, there is no attempt to summarize the tables of the asymmetry truncation normal distribution due to the requirement of huge number of pages. In this paper, the case of asymmetry truncation is included. Second, the methodology provided in this research can be used to summarize similar large tables.