The Beta-Weibull-X Family of Distributions with some Properties and Applications to Engineering and Health Data when X ∼ Rayleigh Distribution

Generating new statistical distributions that provide sufficient characterization for real-life phenomena such as those in reliability engineering, meteorology, and the health sciences is an important area of concern for the researchers. Many complex real-life phenomena are yet to be optimally characterized by some of the existing methods and this study proposed the Beta Weibull-X (BWei-X) family. The Beta Weibull-Rayleigh (BWR), developed as a family member, has notable distributions in the literature as special cases, moments, and some basic statistical properties were investigated. The parameters of the distribution were estimated by the method of maximum likelihood estimation. Graphical reports show that the failure rates can be declining or increasing, J-shape, bathtub, and inverted bathtub shapes, making it an exciting tool in diverse areas of applications for modeling noisy phenomena with left-skewed, right-skewed, and approximately symmetric features. A systolic blood pressure and engineering dataset was applied to investigate the performance of the model, and the results from data analysis using the R-software justify the significance of the research