A simple algorithm for calculating values for folded normal distribution

Abstract

Folded normal distribution originates from the modulus of normal distribution. In the present article, we have formulated the cumulative distribution function (cdf) of a folded normal distribution in terms of standard normal cdf and the parameters of the mother normal distribution. Although cdf values of folded normal distribution were earlier tabulated in the literature, we have shown that those values are valid for very particular situations. We have also provided a simple approach to obtain values of the parameters of the mother normal distribution from those of the folded normal distribution. These results find ample application in practice, for example, in obtaining the so-called upper and lower α-points of folded normal distribution, which, in turn, is useful in testing of the hypothesis relating to folded normal distribution and in designing process capability control chart of some process capability indices. A thorough study has been made to compare the performance of the newly developed theory to the existing ones. Some simulated as well as real-life examples have been discussed to supplement the theory developed in this article. Codes (generated by R software) for the theory developed in this article are also presented for the ease of application.

Investigating the Distribution of Flatness Measurements in Battery Manufacturing through Empirical Investigation and Statistical Theory

“…Machines 2023, 11, x FOR PEER REVIEW 3 of 15 process data (also known as the absolute normal distribution) under certain conditions. Chatterjee et al [24] provided examples of situations commonly associated with folded normal distributions. These instances encompass measurements pertaining to flatness or straightness, as well as the distance between two objects.…”

“…Wang et al [23] presented the actual measurement and statistical processing of error data to show that the distribution law of shape and position error obeys the folded normal process data (also known as the absolute normal distribution) under certain conditions. Chatterjee et al [24] provided examples of situations commonly associated with folded normal distributions. These instances encompass measurements pertaining to flatness or straightness, as well as the distance between two objects.…”