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The radial distribution function is an important measure because several key thermodynamic properties, such as potential energy and pressure can be calculated from it. For a 3-D system where particles interact via pairwise potentials, the potential energy of the system can be calculated as follows: [ 6 ]
One of the first completely free to use and open source statistical software was R, first released in 2000. [1] Some of the free software packages are from governments, for example Epi Info, which is from CDC [4] (Centers for Disease Control and Prevention). Some other software packages are from smaller or independent organizations or universities.
In directional statistics, the projected normal distribution (also known as offset normal distribution, angular normal distribution or angular Gaussian distribution) [1] [2] is a probability distribution over directions that describes the radial projection of a random variable with n-variate normal distribution over the unit (n-1)-sphere.
In statistical mechanics the Percus–Yevick approximation [1] is a closure relation to solve the Ornstein–Zernike equation. It is also referred to as the Percus–Yevick equation. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. The approximation is named after Jerome K. Percus and George J ...
In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2π). [1] A circular distribution is often a continuous probability distribution , and hence has a probability density , but such distributions can also be ...
In 1993, this was developed into a set of DOS-based computer programs by Paul M. Gahlinger with the assistance of one of the original authors of calculator programs, Prof. JH Abramson [2] that came to be called Pepi (an acronym for "Programs for EPIdemiologists") and evolved, after its fourth version in 2001, [3] into WinPepi (Pepi-for-Windows).
Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, R n), axes (lines through the origin in R n) or rotations in R n. More generally, directional statistics deals with observations on compact Riemannian manifolds including the ...
On the other hand, the von Mises distribution is the stationary distribution of a drift and diffusion process on the circle in a harmonic potential, i.e. with a preferred orientation. [1] The von Mises distribution is the maximum entropy distribution for circular data when the real and imaginary parts of the first circular moment are specified.