 A NEF is an exponential family in which the natural parameter "η" and the natural statistic "T"("x") are both the identity.A distribution in an exponential family with parameter "θ" can be written with probability density function (PDF)
where formula_2 and formula_3 are known functions.A distribution in a natural exponential family with parameter θ can thus be written with PDF
[Note that slightly different notation is used by the originator of the NEF, Carl Morris.