Box-Cox transformation of firm size data in statistical analysis

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Chen, Ting Ting^1 ; Takaishi, Tetsuya^2

Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan^1

Hiroshima University of Economics, Hiroshima 731-0192, Japan^2

关键词: Box Cox transformation;    Firm size;    Log transformation;    Log-normal distribution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012182/pdf
DOI  :  10.1088/1742-6596/490/1/012182

来源: IOP

【 摘 要 】

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions.