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:<math>f(x;\mu, k,\theta) \propto \exp{\left(\frac{(x-\mu)^2}{4\theta^2}\right)}D_{-2k-1}\left(\frac{|x-\mu|}{\theta}\right)\,\!</math>,
where ''D'' is a [[parabolic cylinder function]].<ref name=SCB>http://www.newton.ac.uk/programmes/SCB/seminars/121416154.html {{dead link}} </ref>
As for the [[Laplace distribution]], the pdf of the NEG distribution can be expressed as a mixture of [[normal distribution]]s,
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