Identifying unimodal finite mixture models in data sets using distribution shifting – A novel approach

• There are tests for bimodal distributions. • There are no tests for identifying unimodal finite mixture distributions. • We present a method for identifying unimodal finite mixture distributions. • Identifying sub-distributions in finite mixture models can have significance. Finite mixture models represent data distributions composed of several overlapping sub-distributions instead of a single distribution. However, there are few methods and statistical tests for examining the distribution of variables in experimental data to determine if they arise from single or multiple distributions. The unimodal finite mixture model is identified as a type of data set for which little if any statistical approach exists. The morphology (size and shape) of a particle or cell is often important in the analysis of physical or physiological processes, often expressed as a distribution. These variables may be represented by either a single distribution or several distributions represented by a finite mixture model. In this work, number and volume distributions used in morphological analysis are investigated relating to the question of unimodal single distributions compared to finite mixture models. We derived and generalized a mathematical relationship between the number and volume distribution. We show that applying a variate-dependent weight to a unimodal data distribution (number) should result in a shifted unimodal distribution (area or volume). However, if the number data distribution is represented by more than one distribution, the transformed function can result in deformation of the volume distribution and possibly the appearance of additional modes as compared to a single distribution. We developed a novel method that can aid in identifying data distributions which may be unimodal finite mixture models. We applied this approach to simulated data and data sets from two published experiments to demonstrate its use with real data.