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Entropy 2013, 15(11), 4634-4647; doi:10.3390/e15114634
Article

Law of Multiplicative Error and Its Generalization to the Correlated Observations Represented by the q-Product

Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi, Inage, Chiba,Chiba 263-8522, Japan
Received: 8 September 2013 / Revised: 6 October 2013 / Accepted: 21 October 2013 / Published: 28 October 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
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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.
Keywords: multiplicative error; law of error; likelihood function; log-normal distribution; q-product multiplicative error; law of error; likelihood function; log-normal distribution; q-product
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Suyari, H. Law of Multiplicative Error and Its Generalization to the Correlated Observations Represented by the q-Product. Entropy 2013, 15, 4634-4647.

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