Normal-exponential-gamma distribution
Parameters | μ ∈ R — mean (location) shape scale | ||
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Support | |||
Mean | |||
Median | |||
Mode | |||
Variance | for | ||
Skewness | 0 |
In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions. It has a location parameter , scale parameter and a shape parameter .
Probability density function
The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to
- ,
where D is a parabolic cylinder function.[1]
As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions,
where, in this notation, the distribution-names should be interpreted as meaning the density functions of those distributions.
Within this scale mixture, the scale's mixing distribution (an exponential with a gamma-distributed rate) actually is a Lomax distribution.
Applications
The distribution has heavy tails and a sharp peak[1] at and, because of this, it has applications in variable selection.
See also
References
- ^ a b http://www.newton.ac.uk/programmes/SCB/seminars/121416154.html [dead link]
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univariate
with finite support | |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- Multinomial
- Continuous:
- Dirichlet
- Multivariate Laplace
- Multivariate normal
- Multivariate stable
- Multivariate t
- Normal-gamma
- Matrix-valued:
- LKJ
- Matrix normal
- Matrix t
- Matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- Univariate von Mises
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- Bivariate (spherical)
- Kent
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- Bivariate von Mises
- Multivariate
- von Mises–Fisher
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and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
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