## 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!

## List of Statistical Distributions

Click any of the distributions for more information.

- Bates Distribution.
- Bernoulli Distribution
- Beta Binomial Distribution
- Beta Distribution.
- Beta Geometric Distribution (Type I Geometric)
- Binomial Distribution.
- Bimodal Distribution.
- Bivariate Normal Distribution.
- Bradford Distribution
- Burr Distribution.
- Categorical Distribution
- Cauchy Distribution.
- Compound Probability Distribution
- Continuous Probability Distribution
- Cumulative Frequency Distribution
- Cumulative Distribution Function
- Degenerate Distribution.
- Dirichlet Distribution.
- Discrete Probability Distribution
- Empirical Distribution Function
- Erlang Distribution.
- Exponential 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.
- Generalized Error Distribution.
- Geometric Distribution.
- Gompertz Distribution.
- Heavy Tailed Distribution
- Hypergeometric Distribution.
- Inverse Gaussian Distribution.
- Inverse Normal
- J Shaped Distribution.
- Kent Distribution
- Kumaraswamy Distribution
- Landau Distribution
- Laplace Distribution.
- Lévy Distribution.
- Lindley Distribution.
- Lognormal Distribution.
- Lomax Distribution.
- Long Tail Distribution.
- Marginal Distribution
- Mixture Distribution
- Multimodal Distribution.
- Multinomial Distribution.
- Multivariate Normal Distribution.
- Nakagami Distribution.
- Negative Binomial Distribution
- Normal Distribution.
- Open Ended Distribution
- Pareto Distribution.
- Pearson Distribution.
- PERT Distribution.
- Poisson Distribution.
- Power Law Distribution
- Rayleigh Distribution.
- Reciprocal Distribution.
- Relative Frequency Distribution
- Rician Distribution.
- Skewed Distribution
- Stable Distribution
- Symmetric Distribution
- T Distribution.
- Trapezoidal Distribution.
- Triangular Distribution.
- Truncated Normal Distribution.
- Tukey Lambda Distribution.
- Tweedie Distribution.
- Uniform Distribution.
- Unimodal Distribution.
- U-Shaped Distribution.
- Von Mises Distribution.
- Wallenius Distribution.
- Waring Distribution.
- Weibull Distribution.
- Wishart Distribution.
- Yule-Simon Distribution
- Zeta Distribution.

See also:

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*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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