ewm_mean_by documented formula for the decay parameter is incorrect

[sharky564]

Description

The formula supplied for $\alpha_i$ is currently incorrect. For small time intervals, it would imply that $\alpha_i$ is close to $1$, so the ewm would be very close to the current value, which is not the expected behaviour of ewms. Instead, $\alpha_i = 1 - \exp(-\lambda (t_i - t_{i-1}))$ would yield the correct behaviour (and is indeed what is shown in ewm_mean documentation, as well as pandas documentation for ewm).

Link

https://docs.pola.rs/api/python/stable/reference/expressions/api/polars.Expr.ewm_mean_by.html

[MarcoGorelli]

thanks @sharky564 - I think you're right, there's a missing 1- in the docs