feat: add stats/base/dists/bradford/median

[anandkaranubc]

Progresses towards resolving #168

Description

What is the purpose of this pull request?

This pull request:

• Adds the JS implementation of the median of a Bradford distribution.

Related Issues

Does this pull request have any related issues?

This pull request:

• progresses RFC: add the Bradford distribution #168

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

No.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

---

@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/bradford/median	$\color{green}115/115$ $\color{green}+100.00\%$	$\color{green}6/6$ $\color{green}+100.00\%$	$\color{green}1/1$ $\color{green}+100.00\%$	$\color{green}115/115$ $\color{green}+100.00\%$

The above coverage report was generated for the changes in this PR.

[anandkaranubc]

Similar comment to the mean implementation:

The tolerance had to be slightly increased due to differences in the sqrt( 1 + c ) calculations when c was close to 0 while testing it against SciPy-generated test fixtures.

[anandkaranubc]

This is more noticeable when c is close to 0.

In our case, specifically when c = 0.1

[anandkaranubc]

FYI, the formula for the median was derived using the formula of the CDF of the Bradford distribution and equating it to 0.5:

$$F(m_d; c) = 0.5$$

where

$$F(x; c) = \frac{\ln(1 + c x)}{\ln(1 + c)}$$

which gives:

$$m_d = \frac{\sqrt{1 + c} - 1}{c}$$

or in exact terms:

$$m_d = \frac{\log(0.5 * \exp(1+c)) - 1}{c}$$

I used both of the above formulas to check if they reduce the tolerance. There was no difference, and the second one is also very computationally expensive.

[Planeshifter]

One small edit, otherwise all good!

[anandkaranubc]

One small edit, otherwise all good!

Thanks @Planeshifter. I will make the same change to other PRs too (right away).

[stdlib-bot]

PR Commit Message

feat: add `stats/base/dists/bradford/median`

PR-URL: https://github.com/stdlib-js/stdlib/pull/5275

Co-authored-by: Karan Anand <[email protected]>
Co-authored-by: Philipp Burckhardt <[email protected]>
Signed-off-by: Philipp Burckhardt <[email protected]>

Please review the above commit message and make any necessary adjustments.