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Overview of the Statistics Package

 The Statistics package is a collection of tools for mathematical statistics and data analysis. The package supports a wide range of common statistical tasks such as quantitative and graphical data analysis, simulation, and curve fitting.
 • In addition to standard data analysis tools the Statistics package provides a wide range of symbolic and numeric tools for computing with random variables. The package supports over 35 major probability distributions and provides facilities for defining new distributions.
 • Much of the functionality in the Statistics package is accessible through the Context Panel. Context-sensitive functionality is available when selecting any data container (such as a Vector, list, or Array), known probability distributions (such as Normal(1,2)), or random variables.
 • Some related functionality regarding time series is available through the TimeSeriesAnalysis package.
 • For additional examples detailing the uses of the Statistics package, see the following example worksheets.

 • Below is the list of primary topics. See also Statistics[Commands] for an alphabetical list of Statistics commands.
 • Each command in the Statistics package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 • The long form, Statistics:-command, is always available.

Inventory of Probability Distributions

 • Over 35 continuous and discrete probability distributions as well as tools for creating new distributions. Here is the list of relevant commands.

 Bernoulli distribution beta distribution binomial distribution Cauchy distribution chi-square distribution discrete uniform distribution create a non-integer discrete distribution create new distribution empirical distribution Erlang distribution error (exponential power) distribution exponential distribution Fisher f-distribution gamma distribution geometric distribution Gumbel distribution hypergeometric distribution inverse Gaussian (Wald) distribution Laplace distribution logistic distribution log normal distribution Maxwell distribution Moyal distribution negative binomial (Pascal) distribution noncentral beta distribution noncentral chi-square distribution noncentral f-distribution noncentral t-distribution normal (Gaussian) distribution Pareto distribution Poisson distribution power distribution probability table Rayleigh distribution Student-t distribution triangular distribution uniform (rectangular) distribution von Mises distribution Weibull distribution

 • More information is available in the Statistics[Distributions] help page.

Descriptive Statistics, Data Summary and Tabulation

 • A wide range of functions for computing descriptive statistics. This includes location, dispersion and shape statistics, moments and cumulants, as well as several data summary and tabulation commands. Here is the list of available commands.

 compute the average absolute deviation autocorrelations central moments correlation/correlation matrix covariance/covariance matrix cross-correlations cumulants seven summary statistics deciles compute expected values five-point summary frequency table geometric mean harmonic mean Hodges-Lehmann statistic interquartile range kurtosis generate a procedure for calculating statistical quantities arithmetic mean average absolute deviation from the mean median compute the median absolute deviation mode moments order statistics principal component analysis percentiles principal component analysis quadratic mean quantiles quartiles range Rousseeuw and Croux' Qn Rousseeuw and Croux' Sn skewness standard deviation standard error of the sampling distribution standardized moments trimmed mean variance coefficient of variation winsorized mean

 • More information is available in the Statistics[DescriptiveStatistics] help page.

Probability Calculations, Random Variables

 • Tools for creating and manipulating random variables as well as functions for computing their densities, moments, generating functions and other quantities. Here is the list of available commands.

 compute the average absolute deviation cumulative distribution function central moments cumulant generating function characteristic function cumulants cumulant generating function cumulative distribution function deciles compute expected values hazard (failure) rate geometric mean harmonic mean hazard (failure) rate Hodges-Lehmann statistic interquartile range inverse survival function kurtosis generate a procedure for calculating statistical quantities arithmetic mean average absolute deviation from the mean median compute the median absolute deviation moment generating function Mills ratio mode moments moment generating function order statistics probability density function percentiles compute the probability of an event probability density function probability function quadratic mean quantiles quartiles create new random variable Rousseeuw and Croux' Qn Rousseeuw and Croux' Sn skewness standard deviation standard error of the sampling distribution standardized moments support set of a random variable survival function variance coefficient of variation

 • More information is available in the Statistics[RandomVariables] help page.

Visualization

 • Various statistical plots such as box plots, bar charts, histograms, probability plots, scatterplots, etc. Here is the list of available commands.

 generate agglomerated plots create area charts from data create bar charts from data generate biplots create box plots from data generate bubble plots create column graphs from data create autocorrelation plot from data generate cumulative sum charts plot the density of a random variable generate error plots generate frequency plots generate a grid of plots generate heat maps generate histograms plot the kernel density estimate of a data set generate line charts generate normal plots generate Pareto chart generate pie charts generate point plots generate probability plots plot a profile of the likelihood function plot a profile of the log likelihood function generate quantile-quantile plots generate scatter plots generate 3D scatter plots generate scree plots for variance generate sunflower plots generate surface plots generate symmetry plots generate tree maps generate Venn diagrams create violin plots from data generate Weibull plots

 • More information is available in the Statistics[Visualization] help page.

Simulation

 • Optimized algorithms for simulating from all supported distributions as well as tools for creating custom random number generators, parametric and non-parametric bootstrap. Here is the list of available commands.

 compute bootstrap statistics sample a kernel density estimate generate random sample

 • More information is available in the Statistics[Simulation] help page.

Regression

 • Tools for fitting linear and nonlinear models to data points and performing regression analysis. Here is the list of available commands.

 fit an exponential function to data fit a model function to data robust linear regression fit a linear model function to data fit a logarithmic function to data produce lowess smoothed functions fit a nonlinear model function to data generate a one-way ANOVA table fit a polynomial to data fit a power function to data fit a predictive linear model function to data robust linear regression

 • More information is available in the Statistics[Regression] help page.

Estimation

 • Tools for manipulating likelihood functions, maximum likelihood estimation, kernel density estimation, bootstrap. Here is the list of available commands.

 Fisher information statistical information estimate the probability density of a data set likelihood function compute the likelihood ratio statistic log likelihood function compute the maximum likelihood estimate statistical score

 • More information is available in the Statistics[Estimation] help page.

Data Manipulation

 • Tools for manipulating statistical data. Here is the list of available commands.

 compute number/total weight of observations compute number/total weight of missing values compute cumulative products compute cumulative sums remove any trend from a set of data compute lagged differences between elements evaluate data using floating-point arithmetic remove data items based on density join data samples order data items according to their ranks rank data items according to their numeric values remove data items satisfying a condition remove data items which belong to the given range remove non-numeric values center and/or scale a set of data select data items satisfying a condition select data items which belong to the given range select non-numeric values apply random permutation to a data sample sort numeric data split matrix data into submatrices compute data frequencies compute cumulative data frequencies trim data set winsorize data set

 • More information is available in the Statistics[DataManipulation] help page.

Data Smoothing

 • Data smoothing functions including moving averages, exponential smoothing, linear filters, etc. Here is the list of available commands.

 apply exponential smoothing to a data set apply linear filter to a data set compute moving averages for a data set compute moving medians for a data set compute moving statistics for a data set compute weighted moving averages for a data set

 • More information is available in the Statistics[DataSmoothing] help page.

Hypothesis Testing and Inference

 • Common tools for performing hypothesis testing and inference, including several parametric and non-parametric tests.  Here is the list of available commands.

 apply the chi-square test for goodness-of-fit apply the chi-square test for independence in a matrix apply the chi-square suitable model test apply the one sample chi-square test for the population standard deviation apply the one sample t-test for the population mean apply the one sample z-test for the population mean apply Shapiro and Wilk's W-test for normality apply the two sample F-test for population variances apply the paired t-test for population means apply the two sample t-test for population means apply the two sample z-test for population means

 • More information is available at the Statistics[Tests] help page.