DeepFit: automated distribution fitting for building stochastic modelsDeepFit: automated distribution fitting for building stochastic models

Published

April 22, 2022

Author(s)

Siham Khoussi, N. Alan Heckert, Saddek Bensalem, Abdella Battou

Abstract

Statistical model checking (SMC) is a formal verification method that combines simulations with statistical techniques to provide quantitative answers on whether a stochastic system satisfies some requirements with a controllable accuracy. SMC takes three inputs: a stochastic model, a linear-time/Metric Temporal Logic property to verify and a set of required confidence parameters. The stochastic model is generally obtained by modeling the functional behavior of a system then adding probabilistic variables to it, which are updated via probability distributions (PD). The latter is, typically, obtained by analyzing measurements from the system's execution using statistical tests to select the best fit distribution. However, this task requires a good statistical background and familiarity with several distributions which is beyond the expertise of some analysts. Hence, in the case of SMC, assuming an incorrect distributional model for the data can lead to inappropriate statistical analysis as well as inaccurate verification of the system under study. As such, this paper presents DeepFit, a tool that uses deep learning in addition to traditional statistics to automate the distributional modeling process. DeepFit was evaluated against synthetic data and real world data and it can perform comparably to using maximum likelihood estimation with an Anderson-Darling, Kolmogorov-smirnov and Probability plot correlation coefficient plot goodness of fit testss

Citation

Technical Note (NIST TN) - 2218

Report Number

2218

NIST Pub Series

Technical Note (NIST TN)

Pub Type

NIST Pubs

Download Paper

https://doi.org/10.6028/NIST.TN.2218

Local Download

Keywords

Deep learning, Statistical model checking, data analysis, distribution fitting

Citation

Khoussi, S. , Heckert, N. , Bensalem, S. and Battou, A. (2022), DeepFit: automated distribution fitting for building stochastic modelsDeepFit: automated distribution fitting for building stochastic models, Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.TN.2218, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934106 (Accessed October 9, 2025)