ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density

Abstract

The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done.

Keywords: ex-Gaussian fit; python; response components; response times; significance testing.

Figure 1

ex-Gaussian distributions for different values of the λ asymmetry parameter.

Figure 2

Differences between the ex-Gaussian distribution with λ = 0.2 and the gaussian distribution. Both curves plotted on the left and the difference on the right (note this difference is less than 1%).

Figure 3

Data for the young_gng experiment trimmed for outliers with three fitted ex-Gaussians.

Figure 4

Fitting results obtained with the minSQR method varying the number of intervals in the histogram for the young_hfgng experiment. The horizontal line shows the value obtained with the maxLKHD method. (Upper left) Evolution of the p probability. (Upper right) Evolution of μ. (Bottom left) Evolution of σ. (Bottom right) Evolution of τ.