Statistics Toolbox provides functions and an app to work with parametric and nonparametric probability distributions. With these tools, you can:
The Distribution Fitting Tool in the toolbox enables you to fit data using predefined univariate probability distributions, a nonparametric (kernel-smoothing) estimator, or a custom distribution that you define. This tool supports both complete data and censored (reliability) data. You can exclude data, save and load sessions, and generate MATLAB code.
You can estimate distribution parameters at the command line or construct probability distributions that correspond to the governing parameters.
Additionally, you can create multivariate probability distributions, including Gaussian mixtures and multivariate normal, multivariate t, and Wishart distributions. You can use copulas to create multivariate distributions by joining arbitrary marginal distributions using correlation structures.
See the complete list of supported distributions.
With the toolbox, you can specify custom distributions and fit these distributions using maximum likelihood estimation.
Statistics Toolbox provides statistical plots to evaluate how well a dataset matches a specific distribution. The toolbox includes probability plots for a variety of standard distributions, including normal, exponential, extreme value, lognormal, Rayleigh, and Weibull. You can generate probability plots from complete datasets and censored datasets. Additionally, you can use quantile-quantile plots to evaluate how well a given distribution matches a standard normal distribution.
Statistics Toolbox also provides hypothesis tests to determine whether a dataset is consistent with different probability distributions. Specific tests include:
Statistics Toolbox provides functions for analyzing probability distributions, including:
Statistics Toolbox provides functions for generating pseudo-random and quasi-random number streams from probability distributions. You can generate random numbers from either a fitted or constructed probability distribution by applying the random method.
Statistics Toolbox also provides functions for:
You can also generate quasi-random number streams. Quasi-random number streams produce highly uniform samples from the unit hypercube. Quasi-random number streams can often accelerate Monte Carlo simulations because fewer samples are required to achieve complete coverage.