Statistical Analysis of Upper Bound using Data with Uncertainties

Let $F$ be the unknown distribution of a non-negative continuous random variable. We would like to determine if $supp(F) \subseteq [0,c]$ where $c$ is a constant (a proposed upper bound). Instead of directly observing $X_1,...,X_n i.i.d. \sim F$, we only get to observe as data $Y_1,...,Y_n$ where $Y_i = X_i + \epsilon_i$, with $\epsilon_i$ being random variables representing errors. In this paper, we will explore methods to handle this statistical problem for two primary cases - parametric and nonparametric. The data from deep inelastic scattering experiments on measurements of $R=\sigma_L / \sigma_T$ would be used to test code which has been written to implement the discussed methods.