Probability Distribution: List of Statistical Distributions

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.

In a normal distribution, the percentages of scores you can expect to find for any standard deviations from the mean are the same.

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

Click any of the distributions for more information.

• Arcsine Distribution
• 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
• Copula Distributions
• 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
• Hyperexponential Distribution
• Hypergeometric Distribution.
• Inverse Gaussian Distribution.
• Inverse Normal
• Irwin–Hall Distribution
• 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
• Non-Central Distribution
• Normal Distribution.
• Open Ended Distribution
• Pareto Distribution.
• Pearson Distribution.
• PERT Distribution.
• Phase Type Distribution
• Poisson Distribution.
• Power Law Distribution
• Rayleigh Distribution.
• Reciprocal Distribution.
• Relative Frequency Distribution
• Rician Distribution.
• Robust Soliton Distribution
• Severity 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.
• Univariate Distribution
• U-Shaped Distribution.
• Von Mises Distribution.
• Von Mises Fisher Distribution
• Wallenius Distribution.
• Waring Distribution.
• Weibull Distribution.
• Wishart Distribution.
• Yule-Simon Distribution
• Zeta Distribution.

See also:

• Infinite Variance.

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