On the Weighted 2-Parameter Rayleigh Distribution

The role of Weighted Distribution in statistical modeling is influenced by a particular weighting mechanism. This paper introduces the Weighted Two-Parameter Rayleigh (W2R) distribution, an extension of the Rayleigh distribution, achieved by extending the baseline distribution by using an inverted weight function with an additional parameter. This modification provides greater flexibility, making the W2R distribution more suitable for diverse applications in reliability analysis and survival studies modeling. Theoretical and statistical properties of the new weighted distribution such as survival function, hazard function, reversed hazard function, moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, harmonic mean, moment generating function, mean-deviation, Rényi entropy, and order statistics were explicitly derived. This was to assess the flexibility and applicability of W2RD, moments, and the associated measures of W2RD distribution. The new weighted Rayleigh distribution parameters were estimated using the Maximum Likelihood Estimation (MLE) performance evaluators. A comparative analysis of W2R distribution with other existing distributions using remission time analysis was applied to two real-life datasets to evaluate its effectiveness. The models performances were assessed using Log-Likelihood and Akaike Information Criterion (AIC) and the results indicated that the W2R distribution provides a superior fit to real-world data compared to competing distributions. The study therefore highlights the potential of the W2R distribution as a more robust and versatile alternative for statistical modeling in various fields.