Contents:

Definition of a Probability Distribution

A to Z List of Distributions

## What is a Probability Distribution?

A probability distribution tells you what the probability of an event happening is. Probability distributions can show **simple events**, like tossing a coin or picking a card. They can also show much more **complex events**, like the probability of a certain drug successfully treating cancer.

There are many different types of probability distributions in statistics including:

- Basic probability distributions which can be shown on a probability distribution table.
- Binomial distributions, which have “Successes” and “Failures.”
- Normal distributions, sometimes called a Bell Curve.

The sum of all the probabilities in a probability distribution is always 100% (or 1 as a decimal).

### Ways of Displaying Probability Distributions

Probability distributions can be shown in **tables **and **graphs** or they can also be described by a **formula**. For example, the binomial formula is used to calculate binomial probabilities.

The following table shows the probability distribution of a tomato packing plant receiving rotten tomatoes. Note that if you add all of the probabilities in the second row, they add up to 1 (.95 + .02 +.02 + 0.01 = 1).

The following graph shows a standard normal distribution, which is probably the most **widely used probability distribution**. The standard normal distribution is also known as the “bell curve.” Lots of natural phenomenon fit the bell curve, including heights, weights and IQ scores. The normal curve is a continuous probability distribution, so instead of adding up individual probabilities under the curve we say that the total area under the curve is 1.

*Note: *Finding the area under a curve requires a little integral calculus, which you won’t get into in elementary statistics. Therefore, you’ll have to take a leap of faith and just accept that the area under the curve is 1!

## References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.

## List of Statistical Distributions

Jump to A B C D E F G H I J K L M N O P R S T U V W Y Z.

Click any of the distributions for more information.

**A**

- Alpha Distribution
- Arcsine Distribution
- Arfwedson Distribution
- Array Distribution
- Azzalini Distribution

- Bates Distribution.
- Bell Shaped Distribution
- Benford Distribution: Definition, Examples
- Bernoulli Distribution
- Beta Binomial Distribution
- Beta Distribution.
- Beta Geometric Distribution (Type I Geometric)
- Beta Prime Distribution
- Binomial Distribution.
- Bimodal Distribution.
- Birnbaum-Saunders Distribution
- Bivariate Distribution
- Bivariate Normal Distribution.
- Bradford Distribution
- Burr Distribution.

- Categorical Distribution
- Cauchy Distribution.
- Compound Probability Distribution
- Continuous Probability Distribution
- Copula Distributions
- Cosine Distribution
- Cramp Function Distribution
- Cumulative Frequency Distribution
- Cumulative Distribution Function

- Darmois-Koopman Distribution
- Degenerate Distribution.
- De Moivre Distribution
- Dirichlet Distribution.
- Discrete Probability Distribution

- Empirical Distribution Function
- Erlang Distribution.
- Eulerian Distribution
- Exponential Distribution.
- Exponential-Logarithmic Distribution
- Exponential Power Distribution.
- Extreme Value Distribution.

- F Distribution.
- Factorial Distribution
- Fat Tail Distribution.
- Fisk Distribution.
- Folded Normal / Half Normal Distribution.

- G-and-H Distribution.
- Gamma Distribution
- Gamma-Normal Distribution
- Gamma Poisson Distribution
- Generalized Error Distribution.
- Geometric Distribution.
- Gompertz Distribution.
- Gompertz-Makeham Distribution

- Half-Cauchy Distribution
- Half-Logistic Distribution
- Heavy Tailed Distribution
- Hyperbolic Secant Distribution
- Hyperexponential Distribution
- Hypergeometric Distribution.

- Landau Distribution
- Laplace Distribution.
- Lévy Distribution.
- Lindley Distribution.
- Location-Scale Family of Distributions
- Logarithmic Distribution
- Lognormal Distribution.
- Lomax Distribution.
- Long Tail Distribution.

- Marginal Distribution
- Mixture Distribution
- Modified Geometric Distribution
- Multimodal Distribution.
- Multinomial Distribution.
- Multivariate Distribution: Definition
- Multivariate Gamma Distributions
- Multivariate Normal Distribution.
- Muth Distribution

- Nakagami Distribution.
- Negative Binomial Distribution
- Non-Central Distribution
- Noncentral Beta Distribution
- Normal Distribution.

- Parabolic Distribution
- Pareto Distribution.
- Pearson Distribution.
- PERT Distribution.
- Phase Type Distribution
- Pólya Distribution
- Poisson Distribution.
- Power Function Distribution
- Power Law Distribution
- Power Series Distributions

- Rademacher Distribution
- Rayleigh Distribution.
- Reciprocal Distribution.
- Relative Frequency Distribution
- Rician Distribution.
- Robust Soliton Distribution

- Semicircle Distribution
- Severity Distribution
- Sine Distribution
- Skellam Distribution (Poisson Difference Distribution)
- Skewed Distribution
- Special Distribution: Definition, List of
- Stable Distribution
- Standard Power Distribution & U Power Distribution
- Symmetric Distribution

- T Distribution.
- Trapezoidal Distribution.
- Triangular Distribution.
- Truncated Normal Distribution.
- Tukey Lambda Distribution.
- Tweedie Distribution.

See also:

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**Stephanie Glen**. "Probability Distribution: List of Statistical Distributions" From

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