United statistics, confidence quantiles, Bayesian statistics

A survey of research by Emanuel Parzen on how quantile functions provide elegant and applicable formulas that unify many statistical methods, especially frequentist and Bayesian confidence intervals and prediction distributions. Section 0: In honor of Ted Anderson's 90th birthday; Section 1: Quantile functions, endpoints of prediction intervals; Section 2: Extreme value limit distributions; Sections 3, 4: Confidence and prediction endpoint function: Uniform(0,θ)(0,θ), exponential; Sections: 5, 6: Confidence quantile and Bayesian inference normal parameters μμ, σσ; Section 7: Two independent samples confidence quantiles; Section 8: Confidence quantiles for proportions, Wilson's formula. We propose ways that Bayesians and frequentists can be friends!