Neutrosophic Truncated Normal Distribution for Renewable Energy Forecasting and Optimization

Abstract

In this study, a new statistical distribution known as the neutrosophic truncated normal 
distribution is presented for effectively handling indeterminacy and uncertainty in real-world 
datasets, particularly in renewable energy forecasting. Classical truncated normal distribution is 
commonly used for modeling bound phenomena, but it is insufficient to describe inexact, vague or 
conflicting knowledge typically in environmental data. To address this deficiency, the current study 
expands on traditional model by using neutrosophic logic, which considers the truth, 
indeterminacy, and falsity concurrently. Using the maximum likelihood estimation (MLE) 
approach, unknown parameters of the proposed model are estimated. Simulation approach is used 
to validate the reliability of estimated parameters. Simulated results indicate that more reliable 
results can be obtained with larger sample sizes. The key statistical properties of the model, 
including mean, variance, and mode, are derived in the neutrosophic context. The neutrosophic 
structure of some important functions such probability density function (PDF) and cumulative 
distribution function (CDF) are developed. Subsequently, the model is implemented with actual 
wind speeds data for Saudi Arabia. To account for environmental variability and measurement 
uncertainties, the precise wind speed values are transformed into interval-based neutrosophic data. 
The application highlights the practical benefits of the proposed model in renewable energy 
decision-making and optimization, especially in situations with significant uncertainty. 

DOI: 10.5281/zenodo.16887781