In MartinRoth/gpdIcm: Isotonic Scale Estimation of the GPD

The negative log likelihood of the two parameter GPD (location equal to zero) is given by: $$nll(x) = -\log(f_{\xi, \sigma}(x)) = \log(\sigma) + (1 + \frac{1}{\xi}) \log(1 + \frac{\xi x}{\sigma}).$$ The first partial derivative ($\partial \sigma$) is, thus: $$\frac{\partial nll(x)}{\partial \sigma} = \frac{1}{\sigma} - \frac{(\xi + 1) x}{(1 + \frac{\xi x}{\sigma})\sigma^2}$$

MartinRoth/gpdIcm documentation built on May 7, 2019, 3:39 p.m.