/logHazard

Simple functions to compute and visualize logHazard trasform

Primary LanguagePython

logHazard

Simple functions to compute and visualize logHazard trasform.

In order to compute analytical trasform I use Sympy package. In lohH class you will find both .transform and .inverse_transform methods that can be applied to Function classes (from Sympy).

Let $g \in C^1(0,1)$ such that

  • $0 \leqslant g(t) < 1$
  • $g'(t) \geqslant 0$

then we define

$$ logH(g)(s) = \frac{g'(s)}{1-g(s)} $$

$$ logH^{-1}(f)(x) = 1-\exp\left(-\int_a^x \exp \left(f(s)\right) ds \right) $$

Inspired from the paper "Constrained functional time series: Applications to the Italian gas market".