Proxy Variable in OECD Database: Application of Parametric Quantile Regression and Median Based Unit Rayleigh Distribution

This study delves deeply into the captivating world of parametric quantile regression, unveiling the innovative Median Based Unit Rayleigh (MBUR) distribution. This remarkable one-parameter model offers a fresh perspective for statistical analysis, unlocking new pathways for exploration. The estimation process is intricately crafted through a cleverly re-parameterized maximum likelihood function, brought to life with a compelling real-world dataset that animates the theoretical concepts. Moreover, the author takes a comprehensive journey into the realms of inference and goodness of fit, weaving together a rich tapestry of insights that underscore the robust capabilities and adaptability of the MBUR distribution. Recognized for its transformative potential, the MBUR distribution is positioned to reshape analytical practices, garnering widespread acceptance and enthusiasm among statisticians and researchers alike. The author undertook a thorough analysis of real-world data characterized by proportions, which unveiled significant deviations from the assumptions of normality and homoscedasticity. This intricate dataset revealed the presence of outliers, rendering traditional regression methods and generalized linear models unsuitable for effective analysis. In contrast, parametric quantile regression emerged as a robust alternative, gracefully handling the challenges posed by outliers while negating the requirement for normality and accommodating heteroscedasticity. This study, by delving into the complexities of proportionate data, highlights the promising potential of both parametric quantile regression and the median-based unit Rayleigh for insightful and accurate analysis.