This package provides code for finding a beta distribution whose confidence interval is the one you desire. Native to node javascript, it can also be called from other programming languages by querying an endpoint.

Install with:

yarn add fit-beta
# npm install fit-beta

Then set "type": "module", in your package json.

Then:

import {find_beta_from_ci} from 'fit-beta'

let result1 = find_beta_from_ci({ci_lower: 0.3, ci_upper: 0.8})
console.log(result1)

Besides find_beta_from_ci, this package also exports find_beta_from_ci_nelder_mead and find_beta_from_ci_cache, over find_beta_from_ci is just a thin wrapper:

export const find_beta_from_ci = ({ci_lower, ci_upper, ci_length}) => {
  let cache_answer = find_beta_from_ci_cache({ci_lower, ci_upper, ci_length})
  if(cache_answer != null ){
    return cache_answer
  } else {
    let nelder_mead_answer = find_beta_from_ci_nelder_mead({ci_lower, ci_upper, ci_length})
    return nelder_mead_answer
  }
}

find_beta_from_ci_cache is basically instantaneous, but only resolves when ci_lower and ci_upper are in (0.01, 0.02, 0.03, ..., 0.97, 0.98, 0.99, 1), and ci_length is 0.9 (i.e., 90%). find_nelder_mead uses the Nelder Mead algorithm, and will take a bit longer.

Use the bootComb package instead:

# install.packages('bootComb')
library(bootComb)

params <- getBetaFromCI(qLow=0.2,qUpp=0.3,alpha=0.1)$pars
params
# ^ get the parameters of a beta distribution
# whose 90% (1-alpha) confidence interval
# is 0.2 to 0.8

When using in the browser, you could:

• Translate this npm package to use web imports and syntax, etc. The problem with this is that it imports parts of stdlib, which is heavy and from which it is difficult to extract only a small part, because its code is very interconnected.
• Run this in a server, and query the server (this is what I am doing here

You can use this package indirectly in other programming languages by calling an endpoint.

import requests

def get_beta_from_ci(ci_lower, ci_upper, ci_length):
	url = 'https://trastos.nunosempere.com/fit-beta'
	data = {
		"ci_lower": ci_lower,
		"ci_upper": ci_upper,
		"ci_length": ci_length # actually optional
	}
	response = requests.post(url, json = data)
	json_response = response.json()
	return [json_response[0], json_response[1]]

answer = get_beta_from_ci(0.1, 0.8, 0.9)
print(answer)

See also here for caveats.

A simple version might be:

function fitbeta(){

	curl --silent -X POST -H "Content-Type: application/json" \
		-d '{"ci_lower": "'$1'", "ci_upper":"'$2'", "ci_length": "0.95"}' \
		https://trastos.nunosempere.com/fit-beta
}

The version which I'm actually using, which depends on jq and xclip, looks as follows:

function fitbeta(){

	result=$(curl --silent -X POST -H "Content-Type: application/json" \
		-d '{"ci_lower": "'$1'", "ci_upper":"'$2'", "ci_length": "0.95"}' \
		https://trastos.nunosempere.com/fit-beta)
	echo "$result" | jq .
	echo "$result" | sed 's|\[|(|g' | sed 's|\]|)|g' | sed 's|,|, |g' | xclip -sel clip
	echo "(result also copied to keyboard)"

}

Code for this repository is inspired by this package for R. In particular, that package uses R's powerful optim function, and I bothered looking up what optim uses as a default: the Nelder Mead method. I also used that package to populate the cache (see below).

For the Nelder Mead method, I am using this implementation (I tried other algorithms, like BFGS, and implemented a version of backtracking line search, but Nelder Mead proved to just be better). See the nelderMead folder.

For various functions, I am using stdlib. I tried to extract the core code from them, but sadly all of its functions are fairly intertwined.

• Add test coverage
• Add a frontend to this. Now @ nunosempere.com/blog/2023/03/15/fit-beta/.
• ...

Contributions are welcome!

Distributed under the MIT license, except for src/nelderMead, which is distributed under the BSD-3-Clause license, which is satisfied by including the BSD-3-Clause license in the src/nelderMead folder.