Document Type : Original Article
Author
Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran.
Abstract
In this research, we investigate the effect of multiplicative random errors. We build a model which is a physical representation of the multiplicative central limit theorem in mathematical statistics. This theorem demonstrates how the log-normal distribution arises from many minor and multiplicative random effects. A log-normal process is the statistical realization of the multiplicative product of many independent positive random variables. It is always said that the errors in statistical models have a normal distribution, and the reason is that each error component is an effect of an unknown factor. When these components are added together, their sum will have a normal distribution according to the central limit theorem. The total effect of unknown factors is often not additive, and their final effect will be equal to the product of their individual effects. We provide a numerical example and discuss the multiplicative impact on social science.
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