Remove Distributions

[Sbozzolo]

    xp_low = Distributions.quantile(Distributions.Normal(), low_percentile)
    xp_high = Distributions.quantile(Distributions.Normal(), high_percentile)
    return (gauss_int(xp_high) - gauss_int(xp_low)) / max(
        Distributions.cdf(Distributions.Normal(), xp_high) -
        Distributions.cdf(Distributions.Normal(), xp_low),
        eps(FT),
    )

Part of this block is doing nothing.

Distributions.quantile(percentile) computes the x so that the CDF is percentile. Then, Distributions.cdf(x) computes the percentile corresponding to x. The two functions are one the inverse of the other when the same distribution is used.

So, all we need to remove distributions is implement the inverse error function. I used one of the appromation listed on Wikipedia:

Closes #3046

[szy21]

Thanks! The code change looks good to me. I didn't check the math but I trust you and wiki:) Could you check what is the result for percentile_bounds_mean_norm(0.9, 1), and maybe add a test? (I can add the test later if you are busy with other things.)

[Sbozzolo]

Thanks! The code change looks good to me. I didn't check the math but I trust you and wiki:) Could you check what is the result for percentile_bounds_mean_norm(0.9, 1), and maybe add a test? (I can add the test later if you are busy with other things.)

I added a test, I just forgot to commit it!