I want to estimate the error my frequency estimation has.

I used FFT with a window on a series with 3954 samples, sampled at 40 Hz. I know I can calculate the frequency resolution after Rayleigh's theory as $f\_S/N=0.0101 Hz$. However, I found nowhere that this is actually an error estimation of the frequency, and the window used seems to also influence this error. Plus, I need to know with which probability the real frequency lies within my error limits.

Meaning, I just want to be able to write down error estimates for my frequencies, as for example: $f\_1=0.92 \pm 0.02 Hz$

I searched papers now for a long time, and did not really find anything useful. Most give error estimates of the amplitude. I found this: [Getting an Error Estimate for the Spectrum](https://web.physics.utah.edu/%7Edetar/phys6720/handouts/ft_pg1707/ft_pg1707/node11.html) and another paper stating the error estimated with the Rayleigh formula is actually too big (they propose other formulas [here](https://www.researchgate.net/publication/1905781_A_heuristic_derivation_of_the_uncertainty_for_frequency_determination_in_time_series_data)).

Is there a way to do this?