Misalkan 
adalah peubah acak terdistribusi gamma secara identik dan independen dengan parameter yang tak diketahui 
dan 
. Sehingga 
, dan
![\[ f_x(x_1, x_2, \hdots, x_n ; \alpha, \beta)=\frac{\beta^{n\alpha}}{(\Gamma(\alpha))^n}\prod^{n}_{i=1} x^{\alpha-1}_i e^{-\beta \sum^n_{i=1} x_i} \]](http://teknoindonesia.com/wp-content/ql-cache/quicklatex.com-23fac2cc7f495b50f73f751f36dccd84_l3.png "Rendered by QuickLaTeX.com")
persamaan tersebut akan memberikan fungsi log-kemungkinan berupa
![\[ L(x_1,x_2,\hdots,x_n;\alpha,\beta)&=& \log{f_x(x_1,x_2,\hdots,x_n;\alpha,\beta)} \]](http://teknoindonesia.com/wp-content/ql-cache/quicklatex.com-f06a7efde41329e22c4ca6f20f05dd8e_l3.png "Rendered by QuickLaTeX.com")
![\[ &=&n\alpha \log{\beta}-n \log{\Gamma(\alpha)}+(\alpha-1)(\sum^n_{i=1} \log{x_i})-\beta\sum^n_{i=1}x_i \]](http://teknoindonesia.com/wp-content/ql-cache/quicklatex.com-e8ed6275d02301241599a1c1086a7cc3_l3.png "Rendered by QuickLaTeX.com")
dengan melakukan diferensiasi atau turunan terhadap dan , kita akan mendapatkan
![\[ \hat{\beta}_{ML}x_i=\frac{\hat_{\alpha}_{ML}}{\frac{1}{n}\sum^n_{i=1}x_i} \]](http://teknoindonesia.com/wp-content/ql-cache/quicklatex.com-67fe97dfda052418f9e8f4f062de4c16_l3.png "Rendered by QuickLaTeX.com")
![\[ \log{\hat{\alpha}_{ML}}-\frac{\Gamma\'(\hat{\alpha}_{ML})}{\Gamma(\hat{\alpha}_{ML})}=\log{\frac{1}{n}\sum^n_{i=1}x_i}-\frac{1}{n}\sum^n_{i=1}\log{x_i} \]](http://teknoindonesia.com/wp-content/ql-cache/quicklatex.com-356d28d166b8e75ee04bb7f74acdf109_l3.png "Rendered by QuickLaTeX.com")
Untuk estimasi peubah acak tersebut, fungsinya sangat tidak linier.