Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 541, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.physa.2019.123344
Keywords
Probability density function; Cumulative distribution function; Neural networks
Categories
Funding
- National Natural Science Foundation of China [61906043, 61877010, 11501114, 11901100]
- Fujian Natural Science Funds, China [2019J01243]
- Fuzhou University, China [510730/XRC-18075, 510809/GXRC-19037, 510649/XRC-18049, 510650/XRC-18050]
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In order to generate a probability density function (PDF) for fitting the probability distributions of practical data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be utilised as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of the trained deep learning model can be used to estimate the PDF. Numerical experiments with single and mixed distributions are conducted to evaluate the performance of the proposed method. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method. (C) 2019 Elsevier B.V. All rights reserved.
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