Wrapped distributions and measurement errors
Let X be an arbitrary random variable and \(\alpha >0\). For \(x\in R\) one defines \(n_{\alpha}(x):=n\in Z\) iff \(x\in (n\alpha -\alpha /2\), \(n\alpha +\alpha /2)\). The distribution of the deviation \(U_{\alpha}:=n_{\alpha}(X)\alpha -X\) is derived. General criteria for the unimodality of the distribution of \(U_{\alpha}\) are given. The correlation of the measurement errors X-E(X) and \(U_{\alpha}(X)\) is calculated and it occurs to be small. The case of the normal distribution is studied in detail.
scientific article; zbMATH DE number 3872466