Enhanced Statistical Techniques for Weighted Power Rayleigh Distribution with Real-World Applications

The Rayleigh distribution has proven to be a versatile statistical tool, finding applications in fields such as life expectancy studies, reliability analysis and medical research. Similarly, weighted distributions are extensively employed in disciplines like medicine, ecology and reliability studies due to their adaptability in addressing diverse practical scenarios. This study introduces a novel Weighted Power Rayleigh Distribution (WPRD) by applying a weighting mechanism to the Power Rayleigh Distribution, enhancing its applicability in real-world problems where actual statistical data is limited or unavailable. Comprehensive statistical properties, including the mean, variance, moment generating function, skewness, and kurtosis, are derived to provide a deeper understanding of the distribution's characteristics. The research further investigates the distribution function and conducts reliability analysis, emphasizing critical metrics such as survival rate, hazard rate function, and reverse hazard rate. To demonstrate the practical utility of the proposed model, a case study using potato yield data is presented, highlighting its efficacy in agricultural data analysis and prediction. This innovative approach expands the scope of robust statistical modeling and forecasting, offering a valuable framework for applications in various fields. . KEYWORDS :Rayleigh distribution, Weighted Power Rayleigh distribution, Power Rayleigh Distribution, Hazard rate function, Survival rate, Reverse hazard rate function, Potato data, R studio.