On the anti-concentration functions of some familiar families of distributions

Ze-Chun Hu, Renming Song, Yuan Tan

Let $\{X_{\alpha }\}$ be a family of random variables following a certain type of distributions with finite expectation $\mathbf{E}[X_{\alpha }]$ and finite variance $\mathrm{Var}(X_{\alpha })$, where $\alpha$ is…