Input modeling using a computer algebra system

Input modeling that involves fitting standard univariate parametric probability distributions is typically performed using an input modeling package. These packages typically fit several distributions to a data set, then determine the distribution with the best fit by comparing goodness-of-fit statistics. But what if an appropriate input model is not included in one of these packages? The modeler must resort to deriving the appropriate estimators by hand for the appropriate input model. The purpose of this paper is to investigate the use of a prototype Maple-based probability language, known as APPL (A Probability Programming Language), for input modeling. This language allows an analyst to specify a standard or non-standard distribution for an input model, and have the derivations performed automatically. Input modeling serves as an excellent arena for illustrating the applicability and usefulness of APPL. Besides including pre-defined types for over 45 different continuous and discrete random variables and over 30 procedures for manipulating random variables (e.g., convolution, transformation), APPL contains input modeling procedures for parameter estimation, plotting empirical and fitted CDFs, and performing goodness-of-fit tests. Using examples, we illustrate its utility for input modeling