ANOVA
Analysis of variance (ANOVA) permits developers to assign sample variance to various sources and ascertain whether the fluctuation comes up among or amidst various population groups. Statistics Toolbox comprises these ANOVA algorithms and associated techniques:
One-way ANOVA
Two-way ANOVA for balanced data
Multiway ANOVA for unbalanced and balanced data
Analysis of covariance (ANOCOVA)
Nonparametric one-way and two-way ANOVA also known as Kruskal-Wallis and Friedman.
Multiple comparison of slopes, intercepts and group means.
Multivariate ANOVA (MANOVA)
Exploratory Data Analysis
Statistics Toolbox renders various fashions to explore data:descriptive statistics for large data sets, algorithms for cluster analysis and statistical plotting with interactive graphics.
Statistical Plotting and Interactive Graphics
Statistics Toolbox comprises charts and graphs to dig into the data with respect to vision. The toolbox augments MATLAB plot types with box plots, probability plots, scatter histograms, histograms, control charts, quantile-quantile plots and 3D histograms. The toolbox in addition, comprises differentiated plots for multivariate analysis, comprising biplots, dendograms, Andrews plots and parallel coordinate charts.
Descriptive Statistics
Descriptive statistics permits developers to empathize and distinguish potentially prominent sets of data responsively. Statistics Toolbox comprises functions for computing:
Measurements of central tendency comprising median and various means.
Measurements of dispersion comprising range, standard deviation, mean or median absolute deviation and variance.
Linear and rank correlation.
Results established on data with missing values.
Quartile and percentile approximates.
Density approximates employing a kernel-smoothing function.
These functions assists developers sum up values in a data sample employing a few extremely applicable numbers. In some events, approximating summary statistics employing parametric methods is not possible. To address such these cases, Statistics Toolbox renders resampling techniques, comprising:
Extrapolated bootstrap function for figuring sample statistics employing resampling.
Jackknife function for approximating sample statistics employing subsets of the data.
Bootci function for approximating confidence intervals.
Multivariate Statistics
Multivariate statistics render algorithms and functions to canvas multiple variables. Distinctive applications constitute:
Metamorphosing correlated data into a set of uncorrelated components employing centering and rotation (principal component analysis).
Inquire into relationships among variables employing visualization techniques, such as classical multidimensional scaling and scatter plot matrices.
Divide data into segments employing cluster analysis.
Feature Transformation
Feature transformation techniques allow dimensionality step-down when transformed prominent attributes can be more easily ordered than original prominent attributes. Statistics Toolbox permits three classes of characteristic transformation algorithms:
Principal component analysis for summing up data in more a couple of dimensions.
Nonnegative matrix factorization when model terms must constitute nonnegative quantities.
Factor analysis for constructing informative models of data correlation.
Multivariate Visualization
Statistics Toolbox renders charts and graphs to dig into multivariate data visually, comprising:
Dendograms
Scatter plot matrices
Parallel coordinate charts
Biplots
Glyph plots
Andrews plots
Cluster Analysis
Statistics Toolbox permits multiple algorithms for cluster analysis, comprising:
Hierarchical clustering, which produces an agglomerative cluster by and large presented as a tree.
K-means clustering, which attributes data points to the cluster with the nearest mean.
Gaussian mixtures, which are constituted by aggregating multivariate normal density
components. Clusters are attributed by picking out the constituent that make the most of posterior probability.
Probability Distributions
Statistics Toolbox renders graphical and functions tools to work with nonparametric and parametric probability distributions. With these tools, developers can:
Employ statistical plots to assess goodness of fit.
Fit distributions to data.
Give quasi-random number or random streams from probability distributions.
Compute cardinal functions such as cumulative distribution functions and probability density functions.
Fitting Distributions to Data
The Distribution Fitting Tool in the toolbox permits developers to fit data employing a nonparametric (kernel-smoothing) estimator, a custom distribution that developers define or predefined uni variate probability distributions. This tool corroborates both accomplished data and censored data. Developers can keep out data, load and save sessions and compile MATLAB code.
Developers can approximate distribution parameters at the command line or build probability distributions that represent to the controlling parameters. In addition,, developers can produce multivariate probability distributions, comprising multivariate normal and Gaussian mixtures, Wishart distributions and multivariate t. Developers can employ copulatives to produce multivariate distributions by bringing together absolute marginal distributions employing correlation structures.
Evaluating Goodness of Fit
Statistics Toolbox renders statistical plots to measure how well a data set corresponds to a particular distribution. The toolbox comprises probability plots for a diversity of standard distributions, comprising exponential, normal, log normal, extreme value, Weibull and Rayleigh. Developers can bring forth probability plots from censored data sets and accomplished data sets In addition, developers can employ quantile-quantile plots to assess how well a applied distribution copes with a standard normal distribution.
Statistics Toolbox in addition, renders hypothesis tests to determine whether a data set is coherent with various probability distributions. Particular tests constitute:
One-sided and two-sided Kolmogorov-Smirnov tests
Jarque-Bera tests
Chi-Square goodness-of-fit tests
Ansari-Bradley tests
Lilliefors tests
Canvassing Probability Distributions
Statistics Toolbox renders functions for canvassing probability distributions, comprising:
Cumulative density functions
Probability density functions
Negative log-likelihood functions
Inverse cumulative density functions
Bring into existence Random Numbers
Statistics Toolbox renders functions for bringing forth quasi-random and pseudo-random number streams from probability distributions. Developers can bring forth random numbers from either a constructed or fitted probability distribution by enforcing the random method.
Statistics Toolbox in addition, renders functions for:
Give random samples from multivariate distributions, such as normal, t, Wishart and copulas.
Sampling from finite populations
Carry out Latin hypercube sampling
Give samples from Johnson and Pearson systems of distributions
Developers can in addition, gve quasi-random number streams. Quasi-random number streams bring forth extremely consistent samples from the unit hypercube. Quasi-random number streams can oftentimes quicken Monte Carlo simulations as more a couple of samples are called for to accomplish everlasting reporting.
Employing Statistics to Study Uncertainty in System Models
Scientists and Engineers trust on models to distinguish system behavior. System models are oftentimes produced and examined under the presumption that the model inputs, determining operating environment and parameters (constants) are known exactly. Every real-world system operates under uncertainty, all the same, and bankruptcy to account for that uncertainty can contribute to incorrect predictions of system behavior.
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