Definite Numerical Integration with Unknown limit

Question

How to solve for small gamma in the integral equation in Scipy ? I recognize it has to be solved with both the numerical integral and a root solver (Newton's method)

$$ \int_{\gamma}^{+\infty}f(x) dx = 0.01 $$

The function f isn't a known analytical function, it is a probability distribution represented by an array of samples of a histogram.

So essentially the integral is :

$$ \sum_{k = \gamma}^{+\infty} f[k] \Delta x \approx 0.01 $$

Answer 1

You might simply sort the data in ascending order, then figure out which value corresponds to the upper 99th percentile. If $y[0], \dots, y[N-1]$ is your sorted data, it'll be $y[I]$ where $I = 0.99 \times N$. This is a simple quantile estimation as mentioned in the comments by Mark Stone.