Generalized Expected Value Of Continuous Random Variables And Its Applications

In this work, we develop a generalized expected value (GE) of a continuous random variable and propose a novel estimate of GE. Asymptotic normality of this estimator (namely "KWA") is established and a consistent estimate of the asymptotic variance is given. The relationships between KWA and other existing estimators of central tendency such as sample mean, median, trimmed mean and Hodges-Lehmann estimate are studied. The estimator is also applied to construct one-sample hypothesis testings and confidence intervals of locations of any unknown distributions.