差分
このページの2つのバージョン間の差分を表示します。
| 両方とも前のリビジョン前のリビジョン次のリビジョン | 前のリビジョン | ||
| research:memos:chi2 [2019/12/19 15:21] – [Exponential function + constant] kobayash | research:memos:chi2 [2019/12/19 17:30] (現在) – kobayash | ||
|---|---|---|---|
| 行 9: | 行 9: | ||
| \begin{align} | \begin{align} | ||
| - | \sum_i \left[ \ln a - \ln(y_i-c) - b x_i \right] = 0\\ | + | \frac{\partial \chi^2 }{\partial a} = \sum_i \left[ |
| - | \sum_i \left[ b x_i^2 + x_i \ln\left( y_i-c\right) - x_i \ln a \right] = 0\\ | + | \frac{\partial \chi^2 }{\partial b} = \sum_i \left[2 b x_i^2 + 2x_i \ln\left( y_i-c\right) - 2x_i \ln a \right] = 0\\ |
| - | \sum_i \left[ \frac{\ln(y_i-c)}{y_i-c} - \frac{\ln a}{y_i-c} + \frac{b x_i}{y_i-c}\right] = 0\\ | + | \frac{\partial \chi^2 }{\partial c} = \sum_i \left[ |
| \end{align} | \end{align} | ||
| 行 22: | 行 22: | ||
| \begin{align} | \begin{align} | ||
| n \ln a \sum_i x_i - \sum_i x_i \sum_i \ln(y_i-c) - b \left(\sum_i x_i\right)^2 = 0\\ | n \ln a \sum_i x_i - \sum_i x_i \sum_i \ln(y_i-c) - b \left(\sum_i x_i\right)^2 = 0\\ | ||
| - | n b \sum_i x_i^2 + n\sum_i x_i \ln\left( y_i-c\right) - n\ln a \sum_i x_i = 0\\ | + | n b \sum_i x_i^2 + n \sum_i x_i \ln\left( y_i-c\right) - n\ln a \sum_i x_i = 0\\ |
| \end{align} | \end{align} | ||
| + | \begin{align} | ||
| + | \left[n \sum_i x_i^2 + \left(\sum_i x_i\right)^2 \right] b = \sum_i x_i \sum_i \ln(y_i-c) - n \sum_i x_i \ln\left( y_i-c\right) \\ | ||
| + | \end{align} | ||
| + | |||
| + | \begin{align} | ||
| + | b = \frac{\sum_i x_i \sum_i \ln(y_i-c) - n \sum_i x_i \ln\left( y_i-c\right)}{n \sum_i x_i^2 + \left(\sum_i x_i\right)^2} \\ | ||
| + | \end{align} | ||
| + | 書きかけ | ||
