A New Neutrosophic Extended Rayliegh Distribution for Enhanced Productivity and Efficiency Across Industrial Sectors: A case study of Al-Kharj region

Fuad S. Al-Duais^1,3, , Walid Aydi ^{*, 2,4}

¹ Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

²Department of Computer Science, College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia

³Business Administration Department, Administrative Science College, Thamar University, Thamar, Yemen

⁴ Laboratory of Electronics & Information Technologies, Sfax University, Sfax, Tunisia

Emails: F.alduais@psau.edu.sa; w.aydi@psau.edu.sa

Abstract

This paper introduces a new statistical distribution called the Neutrosophic Extended Rayleigh Distribution (NERD), which is specifically developed to handle uncertainty commonly found in industrial applications. We conduct a comprehensive examination of the statistical characteristics of NERD, including important measures such as the quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, uncertainty measures, distributions of order statistics, and L-moments. Parameter estimation is conducted by maximum-likelihood estimation within a neutrosophic framework, guaranteeing resilient inference in practical situations. Through the application of NERD to actual industrial datasets, we evaluate its adaptability and efficiency in simulating industrial processes. A real case study of Al-Kharj region demonstrates the higher performance of NERD. This research highlights the capacity of NERD to greatly improve productivity and efficiency in several industrial sectors.

Keywords: Rayleigh distribution; neutrosophic probability; neutrosophic distribution; solar industry; renewable energy; Al-Kharj