Bayesian Neural Network-Assisted Parameter Estimation of the Transmuted Teissier Distribution for Environmental Data Modeling

Machine learning has evolved into a potent tool for analysing patterns and making predictions from complex data. In this machine learning era, we employed neural network techniques to estimate the parameters of statistical distributions. A primary advantage of probability distribution is its capacity to represent and analyse data effectively. Due to the complexity of the data, classical distributions are generalised or expanded to enhance the flexibility of the probability distributions. This study suggests that the modified Teissier distribution presented in this article serves as a more adaptable model of the Teissier distribution for the analysis of environmental data. The parameters of the proposed distribution are estimated utilising three distinct methodologies: Bayesian neural network (BNN), Bayesian estimation, and maximum likelihood estimation method (MLE). The BNN is achieved by combining the Bayesian estimation method with a neural network, indicating that both the BNN and the Bayesian estimation method commence with identical initial steps. The Bayesian estimation method is conducted using the approach of the Markov Chain Monte Carlo technique. The simulation results indicate that the BNN yields more accurate outcomes than the two conventional methods. The new distribution’s validity is assessed using the environmental data sets and compared with the Teissier distribution and two other established distributions. The discriminative metrics demonstrate that the modified Teissier distribution aligns more effectively with the data sets.