Normal-exponential-gamma distribution
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. 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 at  and, because of this, it has applications in variable selection. See also 
 Compound probability distribution
 Lomax distribution

References

Continuous distributions
Compound probability distributions