# Astrostatistics Tools (astropy.stats)¶

## Introduction¶

The astropy.stats package holds statistical functions or algorithms used in astronomy and astropy.

## Getting Started¶

Most tools are fairly self-contained, and include relevant examples in their docstrings.

## Using astropy.stats¶

More detailed information on using the package is provided on separate pages, listed below.

## Reference/API¶

### astropy.stats Package¶

This subpackage contains statistical tools provided for or used by Astropy.

While the scipy.stats package contains a wide range of statistical tools, it is a general-purpose package, and is missing some that are particularly useful to astronomy or are used in an atypical way in astronomy. This package is intended to provide such functionality, but not to replace scipy.stats if its implementation satisfies astronomers’ needs.

#### Functions¶

 akaike_info_criterion(log_likelihood, ...) Computes the Akaike Information Criterion (AIC). akaike_info_criterion_lsq(ssr, n_params, ...) Computes the Akaike Information Criterion assuming that the observations are Gaussian distributed. bayesian_blocks(t[, x, sigma, fitness]) Compute optimal segmentation of data with Scargle’s Bayesian Blocks bayesian_info_criterion(log_likelihood, ...) Computes the Bayesian Information Criterion (BIC) given the log of the likelihood function evaluated at the estimated (or analytically derived) parameters, the number of parameters, and the number of samples. bayesian_info_criterion_lsq(ssr, n_params, ...) Computes the Bayesian Information Criterion (BIC) assuming that the observations come from a Gaussian distribution. binned_binom_proportion(x, success[, bins, ...]) Binomial proportion and confidence interval in bins of a continuous variable x. binom_conf_interval(k, n[, conf, interval]) Binomial proportion confidence interval given k successes, n trials. biweight_location(a[, c, M, axis]) Compute the biweight location. biweight_midvariance(a[, c, M, axis]) Compute the biweight midvariance. bootstrap(data[, bootnum, samples, bootfunc]) Performs bootstrap resampling on numpy arrays. circcorrcoef(alpha, beta[, axis, ...]) Computes the circular correlation coefficient between two array of circular data. circmean(data[, axis, weights]) Computes the circular mean angle of an array of circular data. circmoment(data[, p, centered, axis, weights]) Computes the p-th trigonometric circular moment for an array of circular data. circvar(data[, axis, weights]) Computes the circular variance of an array of circular data. freedman_bin_width(data[, return_bins]) Return the optimal histogram bin width using the Freedman-Diaconis rule histogram(a[, bins, range, weights]) Enhanced histogram function, providing adaptive binnings jackknife_resampling(data) Performs jackknife resampling on numpy arrays. jackknife_stats(data, statistic[, conf_lvl]) Performs jackknife estimation on the basis of jackknife resamples. knuth_bin_width(data[, return_bins, quiet]) Return the optimal histogram bin width using Knuth’s rule. mad_std(data[, axis]) Calculate a robust standard deviation using the median absolute deviation (MAD). median_absolute_deviation(a[, axis]) Calculate the median absolute deviation (MAD). poisson_conf_interval(n[, interval, sigma, ...]) Poisson parameter confidence interval given observed counts rayleightest(data[, axis, weights]) Performs the Rayleigh test of uniformity. scott_bin_width(data[, return_bins]) Return the optimal histogram bin width using Scott’s rule sigma_clip(data[, sigma, sigma_lower, ...]) Perform sigma-clipping on the provided data. sigma_clipped_stats(data[, mask, ...]) Calculate sigma-clipped statistics on the provided data. signal_to_noise_oir_ccd(t, source_eps, ...) Computes the signal to noise ratio for source being observed in the optical/IR using a CCD. vonmisesmle(data[, axis]) Computes the Maximum Likelihood Estimator (MLE) for the parameters of the von Mises distribution. vtest(data[, mu, axis, weights]) Performs the Rayleigh test of uniformity where the alternative hypothesis H1 is assumed to have a known mean angle mu.

#### Classes¶

 Events([p0, gamma, ncp_prior]) Bayesian blocks fitness for binned or unbinned events FitnessFunc([p0, gamma, ncp_prior]) Base class for bayesian blocks fitness functions LombScargle(t, y[, dy, fit_mean, ...]) Compute the Lomb-Scargle Periodogram PointMeasures([p0, gamma, ncp_prior]) Bayesian blocks fitness for point measures RegularEvents(dt[, p0, gamma, ncp_prior]) Bayesian blocks fitness for regular events