On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process
- 作者：Sí ; lvio M. Duarte Queiró ; s ; sdqueiro@gmail.com
- 关键词：Generalised log-Normal ; Kapteyn multiplicative process ; Metabolic networks ; q-product ; Volatility
- 刊名：Physica A
- 出版年：2012
- 期刊代码：138_03784371
- 类别：et
- 出版时间：1 July, 2012
- 卷：391
- 期：13
- 页码：3594-3606
- 文件大小：582 K
摘要
We discuss the modification of the Kapteyn multiplicative process using the -product of Borges [E.P. Borges, A possible deformed algebra and calculus inspired in nonextensive thermostatistics, Physica A 340 (2004) 95]. Depending on the value of the index a generalisation of the log-Normal distribution is yielded. Namely, the distribution increases the tail for small (when ) or large (when ) values of the variable upon analysis. The usual log-Normal distribution is retrieved when , which corresponds to the traditional Kapteyn multiplicative process. The main statistical features of this distribution as well as related random number generators and tables of quantiles of the Kolmogorov-Smirnov distance are presented. Finally, we illustrate the validity of this scenario by describing a set of variables of biological and financial origin.