Parameters μ ∈ R — mean (location)
k
>
0
{\displaystyle k>0\,}
shape
θ
>
0
{\displaystyle \theta >0\,}
scale Support x
∈
(
−
∞
,
∞
)
{\displaystyle x\in (-\infty ,\infty )\!} PDF ∝
exp
(
(
x
−
μ
)
2
4
θ
2
)
D
−
2
k
−
1
(
|
x
−
μ
|
θ
)
{\displaystyle \propto \exp {\left({\frac {(x-\mu )^{2}}{4\theta ^{2}}}\right)}D_{-2k-1}\left({\frac {|x-\mu |}{\theta }}\right)\,\!} Mean μ
{\displaystyle \mu } Median μ
{\displaystyle \mu } Mode μ
{\displaystyle \mu } | ||
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
Contents
Probability density function
The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to
where D is a parabolic cylinder function.
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.
Applications
The distribution has heavy tails and a sharp peak at