Mathematical modelling of transformations of asymmetrically distributed biological data: An application to a quantitative classification of spiny neurons of the human putamen

Abstract Many measurements in biology follow distributions that can be approximated well by the normal distribution. The normal distribution plays an extremely important role in probability theory. However, some of the experimental data in biology are distributed asymmetrically. In order to transform such an asymmetrical distribution into a normal distribution, for which the standard statistical tables can be used for probability analysis of the available data, one must choose suitable transformation functions. We have met this problem when we qualitatively classified the spiny neurons in the adult human putamen. But, if one tries to test a qualitative classification of neurons quantitatively, a considerable class overlap between cells occurs as well as asymmetry often appears in the distributions of the data. We have already offered a method to overcome the overlapping problem when the data distributions are normal. In order to resolve the asymmetry problem in data distribution, we transformed our asymmetrically distributed data into an approximately normal distribution using a family of simple power functions and on a basis of appropriate probability analysis we propose a more acceptable classification scheme for the spiny neurons. The significance of our results in terms of current classifications of neurons in the adult human putamen is discussed.