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List of probability distributions

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Title: List of probability distributions  
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Subject: Probability distribution, Beta distribution, List of probability topics, Distribution fitting, Rayleigh mixture distribution
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List of probability distributions

Many probability distributions are so important in theory or applications that they have been given specific names.

Contents

  • Discrete distributions 1
    • With finite support 1.1
    • With infinite support 1.2
  • Continuous distributions 2
    • Supported on a bounded interval 2.1
    • Supported on semi-infinite intervals, usually [0,∞) 2.2
    • Supported on the whole real line 2.3
    • With variable support 2.4
  • Mixed discrete/continuous distributions 3
  • Joint distributions 4
    • Two or more random variables on the same sample space 4.1
    • Matrix-valued distributions 4.2
  • Non-numeric distributions 5
  • Miscellaneous distributions 6
  • See also 7

Discrete distributions

With finite support

With infinite support

Continuous distributions

Supported on a bounded interval

Supported on semi-infinite intervals, usually [0,∞)

Supported on the whole real line

With variable support

  • The generalized extreme value distribution has a finite upper bound or a finite lower bound depending on what range the value of one of the parameters of the distribution is in (or is supported on the whole real line for one special value of the parameter
  • The generalized Pareto distribution has a support which is either bounded below only, or bounded both above and below
  • The Tukey lambda distribution is either supported on the whole real line, or on a bounded interval, depending on what range the value of one of the parameters of the distribution is in.
  • The Wakeby distribution

Mixed discrete/continuous distributions

Joint distributions

For any set of independent random variables the probability density function of their joint distribution is the product of their individual density functions.

Two or more random variables on the same sample space

Matrix-valued distributions

Non-numeric distributions

Miscellaneous distributions

See also

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