Abstract: Widely used in scientific and engineering domains, the Gamma distribution provides an essential framework for describing waiting-time mechanisms and positively skewed patterns. Achieving accurate parameter estimates is therefore critical for maintaining the reliability of statistical inference and improving predictive performance. In this paper, the classical methods for estimating the gamma distribution are assessed in comparison to a new method of estimation using neural networks. The integration of Artificial Neural Networks (ANN) into the estimation process enabled the development of a streamlined yet robust neural architecture capable of simultaneously inferring the key parameters of the Gamma distribution. This design leverages the ANN’s ability to learn complex nonlinear relationships within the data, allowing the model to capture the underlying distributional structure and perform joint parameter estimation more efficiently than traditional analytical methods. The ANN neural network uses the concept of matching theoretical and sample quantities to estimate gamma parameters using mean, standard deviation, median, skewness and kurtosis. An extensive simulation study was conducted to demonstrate the power of the proposed ANN-based method. Then, the results of the proposed method were compared to MLE and moment-based methods.

Keywords: Gamma distribution parameters, Neural network, Maximum likelihood estimation, Method of moment, parameter estimation, Backpropagation

Pages: 382-390