Probability Distributions and Hypothesis Tests
A probability distribution is a theoretical distribution based on assumptions about a source population. The distribution describes the probabilities of possible outcomes for a random event. A hypothesis test helps you determine if your sample data comes from a population with particular characteristics, such as a particular distribution. Statistics and Machine Learning Toolbox™ provides functionality for working with probability distributions and performing hypothesis tests, including functions that allow you to:
Fit probability distributions to sample data.
Evaluate probability functions, such as pdf and cdf.
Calculate summary statistics, such as mean and median.
Visualize sample data.
Generate random numbers.
Perform hypothesis testing with distribution tests, location tests, or dispersion tests.
For more information, see Working with Probability Distributions and Available Hypothesis Tests.
Probability Distribution Basics
- Working with Probability Distributions
- Compare Multiple Distribution Fits
- Fit Probability Distribution Objects to Grouped Data
- Nonparametric and Empirical Probability Distributions
- Supported Distributions
- Random Number Generation
- Maximum Likelihood Estimation
- Negative Loglikelihood Functions
- Grouping Variables
Categories
- Discrete Distributions
Compute, fit, or generate samples from integer-valued distributions
- Continuous Distributions
Compute, fit, or generate samples from real-valued distributions
- Multivariate Distributions
Compute, fit, or generate samples from vector-valued distributions
- Exploration and Visualization
Plot distribution functions, interactively fit distributions, create plots, and generate random numbers
- Pseudorandom and Quasirandom Number Generation
Generate pseudorandom and quasirandom sample data
- Resampling Techniques
Resample data set using bootstrap, jackknife, and cross validation
- Hypothesis Tests
t-test, F-test, chi-square goodness-of-fit test, and more
Related Information
Featured Examples
Curve Fitting and Distribution Fitting
Perform curve fitting and distribution fitting, and learn when each method is appropriate.
Simulating Dependent Random Variables Using Copulas
Use copulas to generate data from multivariate distributions when there are complicated relationships among the variables, or when the individual variables are from different distributions.
Fitting a Univariate Distribution Using Cumulative Probabilities
Fit univariate distributions using least squares estimates of the cumulative distribution functions. This is a generally-applicable method that can be useful in cases when maximum likelihood fails, for instance some models that include a threshold parameter.
Fit Custom Distributions
Fit a custom distribution to univariate data by using the mle function.
Avoid Numerical Issues When Fitting Custom Distributions
Use advanced techniques with the mle function to avoid numerical issues when fitting a custom distribution. Specifically, you learn how to:
