\(\large{y=ax^2e^{-bx}} \qquad (1)\) |
\(\large{a=} \) | \(\large{b=} \) | \(\large{σ=} \) | |||||||||
\(\large{y_i>} \) | \(\large{σ} \) | |||
\(\large{a=} \) | \(\large{b=} \) |
\(\large{\log y = \log a + 2\log x - bx}\) | |
\(\large{c - xb= \log y - 2\log x} \qquad \left(c=\log a \right) \qquad (2)\) |
\(\large{ A^\mathsf{T}A \begin{bmatrix} c \\ b \end{bmatrix} = A^\mathsf{T}V } \qquad (3) \) |
\(\large{ A= \begin{bmatrix} 1 & -x_1 \\ 1 & -x_2 \\ \vdots & \vdots \\ 1 & -x_n \end{bmatrix} }\) | \(\large{ V= \begin{bmatrix} \log y_1 - 2\log x_1 \\ \log y_2 - 2\log x_2 \\ \vdots \\ \log y_n - 2\log x_n \\ \end{bmatrix} }\) |
\(\large{y_i > tσ \qquad \left(0<= t <= 3 \right) \qquad (4)}\) |