Using Animated Probability Plots to Explore the Suitability of Mixture Models with Two Component Distributions

Abstract

Risk assessors often use different probability plots as a way to assessthe fit of a particular distribution or model by comparing the plotted points to a straight line and to obtain estimates of the parameters in parametric distributions or models. When empirical data do not fall in a sufficiently straight line on a probability plot, and when no other single parametricdistribution provides an acceptable (graphical) fit to the data, the risk assessor may consider a mixture model with two component distributions. Animated probability plots are a way to visualize the possible behaviors of mixture models with two component distributions. When no single parametric distribution provides an adequate fit to an empirical dataset, animated probability plots can help an analyst pick some plausible mixture models for the data based on their qualitative fit. After using animations during exploratory data analysis, the analyst must then use other statistical tools, including but not limited to: Maximum Likelihood Estimation (MLE) to find the optimal parameters, Goodness of Fit (GoF) tests, and a variety of diagnostic plots to check the adequacy of the fit. Using a specific example with two LogNormal components, we illustrate the use of animated probability plots asa tool for exploring the suitability of a mixture model with two component distributions. Animations work well with other types of probability plots, and they may be extended to analyze mixture models with three or more component distributions.