Package csb :: Package statistics |
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# Package statistics

source code

Statistics root package.

This package contains a number of common statistical utilities. Sub-packages provide more specialized APIs, for example csb.statistics.pdf defines the probability density object model.

Submodules
csb.statistics.ars: Adaptive Rejection Sampling (ARS) csb.statistics.maxent: A Maximum-Entropy model for backbone torsion angles. csb.statistics.mixtures: Mixture models for multi-dimensional data. csb.statistics.pdf: Probability density functions. csb.statistics.pdf.parameterized: Probability density functions with support for shared and computed parameters. csb.statistics.rand: Random number generators csb.statistics.samplers: Defines abstract samplers. csb.statistics.samplers.mc: Abstract Monte Carlo samplers. csb.statistics.samplers.mc.multichain: Implements several extended-ensemble Monte Carlo sampling algorithms. csb.statistics.samplers.mc.neqsteppropagator: Propagator class employing stepwise trajectories as used in the NCMC algorithm (Nilmeier et al., "Nonequilibrium candidate Monte Carlo is an efficient tool for equilibrium simulation", PNAS 2011) csb.statistics.samplers.mc.propagators: Provides various deterministic and stochastic propagators. csb.statistics.samplers.mc.singlechain: Various Monte Carlo equilibrium sampling algorithms, which simulate only one Markov chain. csb.statistics.scalemixture: Approximation of a distribution as a mixture of gaussians with a zero mean but different sigmas

Classes
| Cumulative

Functions
autocorrelation(x, n) auto-correlation of a times series | source code
circmean(a, axis=None) Estimate mean of a circular variable | source code
circvar(a, axis=None) Calculate circular variance of a circular variable. | source code
density(x, nbins, normalize=True) Histogram of univariate input data: basically calls numpy's histogram method and does a proper normalization. | source code
entropy(p) Calculate the entropy of p. | source code
geometric_mean(x, axis=None) Returns: geometric mean of x | source code
harmonic_mean(x, axis=None) Returns: harmonic mean of x | source code
histogram2D(x, nbins=100, axes=None, nbatch=1000, normalize=True) Non-greedy two-dimensional histogram. | source code
histogram_nd(x, nbins=100, axes=None, nbatch=1000, normalize=True) Non-greedy n-dimemsional histogram. | source code
kurtosis(x, axis=None) Returns: Sample kurtosis of x | source code
principal_coordinates(D, nd=None) Reconstruction of a multidimensional configuration that optimally reproduces the input distance matrix. | source code
probabilistic_and(p, axis=0) Probabilistic version of AND | source code
probabilistic_or(p, axis=0) Probabilistic version of OR | source code
probabilistic_xor(p, axis=0) Probabilistic version of XOR. | source code
running_average(x, w, axis=None) Calculates a running average for given window size | source code
skewness(x, axis=None) Returns: Sample skewness of x | source code
weighted_median(x, w) Calculates the weighted median, that is the minimizer of argmin {\sum w_i |x_i - \mu|} | source code

Function Details

### autocorrelation(x, n) | source code
auto-correlation of a times series Parameters: `x` (numpy.array) - time series `n` (int) - Maximal lag for which to compute the auto-correlation

### circmean(a, axis=None) | source code
Estimate mean of a circular variable Parameters: `a` - input array `axis` (None or integer) - axis along which mean is calculated

### circvar(a, axis=None) | source code
Calculate circular variance of a circular variable. Parameters: `a` - input array `axis` (None or integer) - axis along which mean is calculated

### density(x, nbins, normalize=True) | source code
Histogram of univariate input data: basically calls numpy's histogram method and does a proper normalization. Parameters: `x` - input numpy array `nbins` (integer) - number of bins `normalize` - if true, histogram will be normalized

### entropy(p) | source code
Calculate the entropy of p. Returns: entropy of p

### geometric_mean(x, axis=None) | source code
Parameters: `x` `axis` - compute the geometric mean along this axis Returns: geometric mean of x

### harmonic_mean(x, axis=None) | source code
Parameters: `x` `axis` - compute the harmonic mean along this axis Returns: harmonic mean of x

### histogram2D(x, nbins=100, axes=None, nbatch=1000, normalize=True) | source code
Non-greedy two-dimensional histogram. Parameters: `x` (numpy array) - input array of rank two `nbins` (integer) - number of bins `axes` (tuple of two one-dimensional numpy arrays) - x- and y-axes used for binning the data (if provided this will be used instead of <nbins>) `nbatch` (integer) - size of batch that is used to sort the data into the 2D grid `normalize` (boolean) - specifies whether histogram should be normalized Returns: 2-rank array storing histogram, tuple of x- and y-axis

### histogram_nd(x, nbins=100, axes=None, nbatch=1000, normalize=True) | source code
Non-greedy n-dimemsional histogram. Parameters: `x` (numpy array) - input array of rank (-1,n) `nbins` (integer) - number of bins `axes` (tuple of two one-dimensional numpy arrays) - axes used for binning the data (if provided this will be used instead of <nbins>) `nbatch` (integer) - size of batch that is used to sort the data into the nD grid `normalize` (boolean) - specifies whether histogram should be normalized Returns: n-rank array storing histogram, tuple of axes

### kurtosis(x, axis=None) | source code
Parameters: `x` - random variables `axis` - compute the kurtosis along this axis Returns: Sample kurtosis of x

### principal_coordinates(D, nd=None) | source code
Reconstruction of a multidimensional configuration that optimally reproduces the input distance matrix. See: Gower, J (1966)

### probabilistic_xor(p, axis=0) | source code
Probabilistic version of XOR. Works only for axis=0.

### running_average(x, w, axis=None) | source code
Calculates a running average for given window size Parameters: `x` - input array `w` (integer) - window size `axis` - axis along which mean is calculated

### skewness(x, axis=None) | source code
Parameters: `x` - random variables `axis` - compute the skewness along this axis Returns: Sample skewness of x

### weighted_median(x, w) | source code
Calculates the weighted median, that is the minimizer of argmin {\sum w_i |x_i - \mu|} Parameters: `x` - input array `w` - array of weights