A Neural Network-Based Approach for Statistical Probability Distribution Recognition

Abstract

The statistical probability distribution of data should be known in advance, so that we can make some statistical inference based on the data and realize what information the data provides. Until now, a nonparametric goodness of fit test has been widely used in probability distribution recognition. However, such a procedure cannot guarantee a precise distribution recognition when only small data samples are available. In addition, the number of the divided groups will influence the results. This study proposes a neural network-based approach for probability distribution recognition. Two types of neural networks, backpropagation and learning vector quantization, are used in classifying normal, exponential, Weibull, Uniform, Chi-square, t, F, and Lognormal distributions. Implementation results demonstrate that the proposed approach outperforms the traditional statistical approach.

Keywords:

• Neural network
• Statistical probability distribution
• Test for goodness of fit

Notes

Notes: 1. The significance level for the critical region of the nonparameteric goodness of fit test was 0.05

2. When the sample size was 5, the accuracy of the nonparameteric goodness of fit test had a gravity error; therefore, it was not presented.