Zhang, ChengMa, Jianpeng2017-05-032017-05-032012Zhang, Cheng and Ma, Jianpeng. "Estimating statistical distributions using an integral identity." <i>The Journal of Chemical Physics,</i> 136, no. 20 (2012) American Institute of Physics: https://doi.org/10.1063/1.4721638.https://hdl.handle.net/1911/94149We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and the mean force can be evaluated as a configuration average. We show that the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114 (2005)]10.1063/1.1829631. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method. The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant-pressure ensemble, a radial distribution function, and a joint distribution of amino acid backbone dihedral angles.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlehttps://doi.org/10.1063/1.4721638