指数型分布族
{\displaystyle {\begin{aligned}h_{\sigma }(x)&={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\exp \left(-{\frac {x^{2}}{2\sigma ^{2}}}\right)\\[4pt]T_{\sigma }(x)&={\frac {x}{\sigma }}\\[4pt]A_{\sigma }(\mu )&={\frac {\mu ^{2}}{2\sigma ^{2}}}\\[4pt]\eta _{\sigma }(\mu )&={\frac {\mu }{\sigma }}.\end{aligned}}}
σ 2 = 1 {\displaystyle \sigma ^{2}=1} 、すなわち η σ ( μ ) = μ {\displaystyle \eta _{\sigma }(\mu )=\mu } の場合、これは正準型となる。