Law of multiplicative error and its generalization to the correlated observations represented by the q-product

Abstract

The law of multiplicative error is presented for independent observations and correlated observations represented by the q-product, respectively. We obtain the standard log-normal distribution in the former case and the log-q-normal distribution in the latter case. Queirós' q-log normal distribution is also reconsidered in the framework of the law of error. These results are presented with mathematical conditions to give rise to these distributions. © 2013 by the authors.