# **`@decidables/prospectable-math`**
Equations for Calculating Cumulative Prospect Theory in [prospectαbλe](https://decidables.github.io/prospectable)
[](https://www.npmjs.com/package/@decidables/prospectable-math)
[](https://github.com/decidables/decidables/blob/main/LICENSE.md)
Helper functions for calculations related to Cumulative Prospect Theory for
[prospectαbλe](https://decidables.github.io/prospectable).
## Usage
### Install
```shell
yarn add @decidables/prospectable-math
```
### Use
```javascript
import CPTMath from '@decidables/prospectable-math';
```
A class providing static functions for calculating Signal Detection Theory equations
## Contents
### `CPTMath`
Single class exposing static functions for CPT calculations. Each function takes values for one or
more variables and returns the value of another variable. The functions are named with a list of the
input variables followed by a '2' followed by the output variable, in camelcase. For example,
`hM2Hr` takes as input the number of hits, `H`, and the number of misses, `M`, and outputs the hit
rate, `HR`
#### Variable names
- x = objective value
- p = probability
- v = subjective value
- w = decision weight
- u = subjective utility
- a = α (alpha, diminishing marginal utility)
- l = λ (lambda, loss aversion)
- g = γ (gamma, probability distortion)
#### Parameters
- a = α (alpha, diminishing marginal utility) [0, 1]
- l = λ (lambda, loss aversion) [0, Infinity)
- g = γ (gamma, probability distortion) [0, 1]
The values offered for parameters are:
- DEFAULT = a recommended default value
- MIN = the minimum value recommended for a UI (not necessarily the lower bound of its interval)
- MAX = the maximum value recommended for a UI (not necessarily the upper bound of its interval)
- STEP = a recommended step size for a UI
- JUMP = a recommended "large" step size for a UI
#### Methods w/implemented equations
- `xal2v(x, a, l)`
- v = if (x >= 0) x^a; if (x < 0) -l * (-x)^a
- `xlv2a(x, l, v)`
- a = if (x >= 0) log(v) / log(x); if (x < 0) (log(-v) - log(l)) / log(-x)
- `xav2l(x, a, v)`
- a = if (x >= 0) 1; if (x < 0) -v / (-x)^a
- `pg2w(p, g)`
- w = p^g / (p^g + (1 - p)^g)^(1 / g)
- `vw2u(v, w)`
- u = Sum_n(v_n * w_n)
- Accepts numbers or equal-length arrays of numbers
## Development
### Features/Bugs/Notes
### Package Scripts
- `yarn lint`
- Lints markdown, scripts and styles
- `yarn test`
- Runs all tests and reports coverage in `test/coverage/`
- `yarn test --watch`
- `yarn test -w`
- Runs all tests in watch mode and reports coverage in `test/coverage/`
- `yarn test `
- Runs tests for a single file and reports coverage in `test/coverage/`
- `yarn test --watch`
- `yarn test -w`
- Runs tests for a single file in watch mode and reports coverage in `test/coverage/`
- `yarn build`
- Builds bundles from `src/` to `lib/`
### File Organization
- `prospectable-elements/`
- `lib/` (Bundles created from `src/` by `build`) **\[autogenerated\]**
- `src/` (Source files)
- `test/` (Testing files)
- `coverage/` (Code coverage results) **\[autogenerated\]**
- `CHANGELOG.md` (Based on conventional commits) **\[autogenerated\]**
- `gulpfile.js` (Tasks for *gulp*)
- `package.json` (Package config for *yarn* and *npm*)
- `README.md` (This file)
- `rollup-stats.html` (Report on js bundle composition and size) **\[autogenerated\]**
## [License](https://github.com/decidables/decidables/blob/main/LICENSE.md)
The content of this project is licensed under [Creative Commons Attribution-ShareAlike 4.0
International License (CC-BY-SA-4.0)](https://creativecommons.org/licenses/by-sa/4.0/) and the
source code of this project is licensed under [GNU General Public License v3.0 or any later version
(GPL-3.0-or-later)](https://www.gnu.org/licenses/gpl-3.0.html).