A **univariate distribution **is the probability distribution of a single random variable. For example, the energy formula (x – 10)^{2}/2 is a univariate distribution because only one variable (x) is given in the formula. In contrast, *bivariate distributions* have two variables and *multivariate distributions *have two or more.

## Types of Univariate Distribution

Hundreds of univariate distributions exist: some are more common than others. Many of these probability distributions are closely connected via transformations, some of which can be inverted. Transformations can include:

- Distribution of order statistic,
- Taking a mixture of random variables,
- Truncating random variables.

The following image shows how some of the major univariate distributions are connected. Discrete distributions are in blue; Continuous distributions are in green. Common sampling distributions are in orange.

**Discrete**:

**Bernoulli Distribution**: a discrete probability distribution for a Bernoulli trial — a random experiment with two outcomes (“Success” or a “Failure”).**Beta binomial distribution**: a mixture of a binomial and beta distribution.- Binomial distribution
- Discrete uniform
- Gamma Poisson
- Hypergeometric
- Logarithm distribution
- Poisson distribution
- Polya distribution
- Power series
- Rectangular
- Zeta / Zipf

Continuous:

- Benford distribution
- Beta distribution
- Erlang
- Error distribution
- Extreme value
- Gamma (generalized)
- Gamma normal distribution
- Gompertz
- Hyperexponential distribution
- Kolmogorov Smirnov distribution
- Laplace
- Log logistic
- Log normal
- Logistic distribution
- Lomax
- Minimax distribution
- Muth distribution
- Noncentral beta distribution
- Normal Distribution
- Pareto distribution
- Rayleigh distribution
- Triangular
- Wald distribution

## References

Leemis, L. & McQueston, J. Teacher’s Corner: Univariate Distribution Relationships. Retrieved February 19, 2021 from Academia.edu https://www.academia.edu/6823496/Univariate_Distribution_Relationships.

Univariate Distribution. Retrieved February 19, 2021 from: http://www.math.wm.edu/~leemis/chart/UDR/about.html

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**Stephanie Glen**. "Univariate Distribution" From

**StatisticsHowTo.com**: Elementary Statistics for the rest of us! https://www.statisticshowto.com/univariate-distribution/

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