A neural networks-based methodology for fitting data to probability distributions

Determining an appropriate distributional model for a univariate measurement process is a common problem in science and engineering. Although a poorly chosen distributional model may suffice for measuring and assessing the uncertainty of averages, this will not be the case for tails of the distribution. In many applications (e.g., reliability), accurate assessment of the tail behavior is more critical than the average. However, distribution fitting can be an exhaustive process that takes time and requires previous knowledge of statistics as well as familiarity with several probability distributions and is, therefore, a difficult task for some analysts. As such, this paper presents an alternative methodology which is based on a combination of neural networks and statistical tests to conduct distribution fitting. First, neural networks are used to map data to a probability distribution. Then, traditional statistics are used to estimate the parameters of the distribution and conduct further assessment on the fitted model. We show that our neural networks can produce robust results and perform comparably to the traditional statistical tests based on synthetic and real-world data.