DOC/MAINT: special: Several updates for tklmbda

[WarrenWeckesser]

See the individual commit messages for details.

[WarrenWeckesser]

Updated docstring: tklmbda

[WarrenWeckesser]

Rebased, and updated the link to the rendered docstring on CircleCI. The segfault in the CirrusCI job musllinux_amd64_test is not related to this PR.

[melissawm]

This looks good to me - out of curiosity, was the missing bounds check creating a bug somewhere?

Also, I noticed both in the tutorial and in the docstring for the Tukey lambda distribution the formatting is still "wrong" (Tukey-Lambda instead of Tukey lambda). I am guessing those fixes can be done in a follow-up - they also look like good first issues :)

[WarrenWeckesser]

Thanks @melissawm.

[...] was the missing bounds check creating a bug somewhere?

If we call it a bug, it is not a very serious bug. The differences would only be noticed at the ends of the support of the distribution, and they are tiny.

Here are some cases where the change makes a noticeable difference. The values at the ends of the support should be 0 and 1. With the main development branch:

In [2]: tklmbda([-1, 1], 1).tolist()
Out[2]: [7.105427357601002e-15, 0.9999999999999929]

In [3]: tklmbda([-4, 4], 0.25).tolist()
Out[3]: [7.105427357601002e-15, 0.9999999999999929]

In [4]: tklmbda([-0.125, 0.125], 8).tolist()
Out[4]: [7.105427357601002e-15, 0.9999999999999929]

With this pull request:

In [2]: tklmbda([-1, 1], 1).tolist()
Out[2]: [0.0, 1.0]

In [3]: tklmbda([-4, 4], 0.25).tolist()
Out[3]: [0.0, 1.0]

In [4]: tklmbda([-0.125, 0.125], 8).tolist()
Out[4]: [0.0, 1.0]

[dschmitz89]

Very illustrative examples. Nitpick: it could be helpful to add a comparison of calling the Tukey lambda CDF via special.tklmbda or scipy.stats.tukeylambda but that is not a must for me.

[WarrenWeckesser]

@dschmitz89, good idea. I added a note at the end of the docstring. You can see the updated docstring at tklmbda

[melissawm]

This looks like a clear improvement so I'll put it in - thanks @WarrenWeckesser !