List of probability distributions

This list of univariate probability distributions gives an overview of the most well-known univariate ( one-dimensional ) probability distributions.

Describe probability distributions of the breakdown of probabilities to the possible outcomes of a random variable. A distinction is made between discrete distributions that are defined on a finite or countable set, and continuous ( continuous ) distributions that are usually defined at intervals.

Discrete distributions can be described by its probability density. This gives for each of the maximum countable number of values ​​of a random variable on the probability that exactly one obtains this value.

For continuous distributions, the probabilities of individual values ​​can not specify, as they always have the chance. However, it is often possible to the probability that a random variable takes on a value in an interval, represented as an integral over a density function (or probability density ):

The continuous distributions included in this list such a representation of a density function is possible.

• 2.1 Continuous uniform distribution ( rectangular distribution, uniform distribution)
• 2.2 Normal distribution ( Gaussian distribution )
• 2.3 Log-normal distribution ( log-normal distribution)
• 2.4 exponential
• 2.5 Chi -square distribution ( chi-square distribution)
• 2.6 Student's t-distribution
• 2.7 F-distribution (Fisher distribution)
• 2.8 Gamma distribution
• 2.9 Beta distribution
• 2:10 Logistic distribution
• 2:11 Weibull distribution
• 2:12 Cauchy distribution ( Cauchy- Lorentz distribution, Lorentz distribution)
• 2:13 Pareto distribution

Discrete Distributions

The tables below summarize the characteristics of the carrier, the probability function, distribution function, expectation and variance of the following discrete distributions together:

• Discrete distributions
• Bernoulli distribution ( zero-one distribution)
• Binomial distribution
• Negative Binomial ( Pascal distribution )
• Geometric distribution
• Hypergeometric Distribution
• Poisson
• Logarithmic distribution

It denotes the ceiling function, the rounding function and one corresponding random variable.

Discrete distributions

Bernoulli distribution ( zero-one distribution)

Binomial distribution

Negative Binomial ( Pascal distribution )

Geometric distribution

Option A

Variant B

Hypergeometric Distribution

Poisson

Logarithmic distribution

Continuous distributions

The tables below summarize the characteristics of carrier density function, distribution function, expectation and variance of the following continuous distributions together:

• Continuous uniform distribution ( rectangular distribution, uniform distribution)
• Normal distribution ( Gaussian distribution )
• Log-normal distribution
• Exponential distribution
• Chi -square distribution ( chi-square distribution)
• Student's t-distribution
• F-distribution (Fisher distribution)
• Gamma distribution
• Beta distribution
• Logistic distribution
• Weibull distribution
• Cauchy distribution ( Cauchy- Lorentz distribution, Lorentz distribution)
• Pareto distribution

Here denote the Gamma function, Beta function and one corresponding random variable with density and distribution function.

Continuous uniform distribution ( rectangular distribution, uniform distribution)

Normal distribution ( Gaussian distribution )

Log-normal distribution ( log-normal distribution)

Exponential distribution

Chi -square distribution ( chi-square distribution)

Student's t-distribution

F-distribution (Fisher distribution)

Gamma distribution

Beta distribution

Logistic distribution

Weibull distribution

Cauchy distribution ( Cauchy- Lorentz distribution, Lorentz distribution)

Pareto distribution