Normal-exponential-gamma distribution
In probability theory and statistics, the normal-exponential-gamma distribution is a three-parameter family of continuous probability distributions. It has a location parameter, scale parameter and a shape parameter .The probability density function 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.
Within this scale mixture, the scale's mixing distribution actually is a Lomax distribution.Applications
The distribution has heavy tails and a sharp peak at and, because of this, it has applications in variable selection.
