Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, Rn), axes (lines through the origin in Rn) or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds including the Stiefel manifold.
The overall shape of a protein can be parameterized as a sequence of points on the unit sphere. Shown are two views of the spherical histogram of such points for a large collection of protein structures. The statistical treatment of such data is in the realm of directional statistics.[1]
The fact that 0 degrees and 360 degrees are identical angles, so that for example 180 degrees is not a sensible mean of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data (in this case, angular data). Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), compass directions, dihedral angles in molecules, orientations, rotations and so on.
^Hamelryck, Thomas; Kent, John T.; Krogh, Anders (2006). "Hamelryck, T., Kent, J., Krogh, A. (2006) Sampling realistic protein conformations using local structural bias. PLoS Comput. Biol., 2(9): e131". PLOS Computational Biology. 2 (9): e131. Bibcode:2006PLSCB...2..131H. doi:10.1371/journal.pcbi.0020131. PMC 1570370. PMID 17002495.
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Directionalstatistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in...
The circular mean is one of the simplest examples of directionalstatistics and of statistics of non-Euclidean spaces. This computation produces a different...
Illustration of the central limit theorem Central limit theorem for directionalstatistics Lyapunov's central limit theorem Martingale central limit theorem...
everywhere, see Lighthill 1958, p.62, Theorem 22 for details. In directionalstatistics, the Dirac comb of period 2 π {\displaystyle 2\pi } is equivalent...
will be approximately normally distributed. Directionalstatistics is the subdiscipline of statistics that deals with directions (unit vectors in Rn)...
In probability theory and directionalstatistics, the von Mises distribution (also known as the circular normal distribution or Tikhonov distribution)...
In probability theory and directionalstatistics, a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping"...
In directionalstatistics, the projected normal distribution (also known as offset normal distribution or angular normal distribution) is a probability...
The Yamartino method is an algorithm for calculating an approximation of the circular variance of wind direction during a single pass through the incoming...
In probability theory and directionalstatistics, a wrapped exponential distribution is a wrapped probability distribution that results from the "wrapping"...
In probability theory and directionalstatistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform...
theorem Central limit theorem for directionalstatistics – Central limit theorem applied to the case of directionalstatistics Delta method – to compute the...
directional derivative for maps between Banach spaces. It is particularly suited for applications in stochastic programming and asymptotic statistics...
In directionalstatistics, the Kent distribution, also known as the 5-parameter Fisher–Bingham distribution (named after John T. Kent, Ronald Fisher, and...
Sometimes known as the Rayleigh z test. Circular distribution Directionalstatistics Kuiper's test Rayleigh distribution Watson test Rayleigh plot Confidence...
In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles...
Jammalamadaka, also known as J.S. Rao, is a statistician specializing in directionalstatistics, Goodness of fit tests, Spacings, and aspects of large sample efficiencies...
bivariate normal distribution. The distribution belongs to the field of directionalstatistics. The general bivariate von Mises distribution was first proposed...
In probability theory and directionalstatistics, a wrapped probability distribution is a continuous probability distribution that describes data points...
In probability theory and directionalstatistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping"...
Riemannian manifold Directionalstatistics – subdiscipline of statisticsPages displaying wikidata descriptions as a fallback: statistics on manifolds List...
Gaussian distribution that underlies the Bingham distribution. Directionalstatistics von Mises–Fisher distribution Kent distribution Bingham, Ch. (1974)...
OBE (born 1935) is an Indian-British statistician specialising in directionalstatistics, multivariate analysis, geostatistics, statistical bioinformatics...
nonnegative-definite matrix. Complex normal ratio distribution Directionalstatistics § Distribution of the mean (polar form) Normal distribution Multivariate...
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