Univariate Discrete Distributions
R2026bA univariate discrete distribution is a probability distribution that contains a single random variable. This variable can assume only a finite, or countably infinite, number of values. For example, in a Bernoulli distribution, the random variable X can assume only the value 0 or 1.
Statistics and Machine Learning Toolbox™ offers several ways to work with univariate discrete distributions:
Create a distribution object and use distribution object functions.
Use distribution-specific functions with specified distribution parameters.
Use the generic distribution functions with the specified distribution name and corresponding parameters.
For more information, see Working with Probability Distributions.
Apps
| Distribution Fitter | Fit probability distributions to data |
Tools
| Probability Distribution Function Tool | Interactive density and distribution plots |
| Random Number Generation Tool | Interactive random number generation |
Functions
Objects
BinomialDistribution | Binomial probability distribution object |
EmpiricalDistribution | Empirical probability distribution object (Since R2025a) |
NegativeBinomialDistribution | Negative binomial distribution object |
PoissonDistribution | Poisson probability distribution object |
Topics
- Nonparametric and Empirical Probability Distributions
Estimate a probability density function or a cumulative distribution function from sample data.
- Bernoulli Distribution
The Bernoulli distribution is a discrete probability distribution with only two possible values for the random variable.
- Binomial Distribution
The binomial distribution models the total number of successes in repeated trials from an infinite population under certain conditions.
- Empirical Distribution
The empirical distribution is a nonparametric estimate of the cumulative distribution function (cdf) for a sample.
- Geometric Distribution
The geometric distribution models the number of failures before one success in a series of independent trials, where each trial results in either success or failure, and the probability of success in any individual trial is constant.
- Hypergeometric Distribution
The hypergeometric distribution models the total number of successes in a fixed-size sample drawn without replacement from a finite population.
- Multinomial Probability Distribution Objects
This example shows how to generate random numbers, compute and plot the pdf, and compute descriptive statistics of a multinomial distribution using probability distribution objects.
- Multinomial Probability Distribution Functions
This example shows how to generate random numbers and compute and plot the pdf of a multinomial distribution using probability distribution functions.
- Negative Binomial Distribution
The negative binomial distribution models the number of failures before a specified number of successes is reached in a series of independent, identical trials.
- Poisson Distribution
The Poisson distribution is appropriate for applications that involve counting the number of times a random event occurs in a given amount of time, distance, area, and so on.
- Uniform Distribution (Discrete)
The discrete uniform distribution is a simple distribution that puts equal weight on the integers from one to N.
- Maximum Likelihood Estimation
The
mlefunction computes maximum likelihood estimates (MLEs) for a distribution specified by its name and for a custom distribution specified by its probability density function (pdf), log pdf, or negative log likelihood function. - Negative Loglikelihood Functions
Find maximum likelihood estimates using negative loglikelihood functions.
Teaching Resources
Fundamentals of Probability Theory
Learn fundamental probability concepts about random processes, sampling, independence, statistical inference, and conditional probability.
