指数型分布族
η = ( μ σ 2 , − 1 2 σ 2 ) T h ( x ) = 1 2 π T ( x ) = ( x , x 2 ) T A ( η ) = μ 2 2 σ 2 + log  | σ | = − η 1 2 4 η 2 + 1 2 log  | 1 2 η 2 | {\displaystyle {\begin{aligned}{\boldsymbol {\eta }}&=\left({\frac {\mu }{\sigma ^{2}}},-{\frac {1}{2\sigma ^{2}}}\right)^{\rm {T}}\\h(x)&={\frac {1}{\sqrt {2\pi }}}\\T(x)&=\left(x,x^{2}\right)^{\rm {T}}\\A({\boldsymbol {\eta }})&={\frac {\mu ^{2}}{2\sigma ^{2}}}+\log |\sigma |=-{\frac {\eta _{1}^{2}}{4\eta _{2}}}+{\frac {1}{2}}\log \left|{\frac {1}{2\eta _{2}}}\right|\end{aligned}}}