# stochastic

> Simple functions for simulating Poisson Processes, Brownian motion, geometric Brownian motion, discrete/continuous-time Markov chains, and normal random variables

Latest version **0.0.14** (published 2015-09-26) · MIT license · 0 weekly downloads

## Install

```sh
npm install stochastic
pnpm add stochastic
yarn add stochastic
bun add stochastic
```

## Health

**Score 15/100 (F)** — status: abandoned.

Positive: no vulnerabilities.

Warnings: low downloads; no types; no esm support; pre 1.0.

Negative: abandoned; low maintenance score.

## Facts

| | |
|---|---|
| Version | 0.0.14 |
| Published | 2015-09-26 |
| First published | 2014-08-06 |
| Weekly downloads | 0 |
| License | MIT |
| TypeScript types | none |
| Module format | CommonJS |
| Dependencies | 0 |
| Known vulnerabilities | 0 |
| Install scripts | no |
| GitHub stars | 235 |
| Author | Nathan Epstein |
| Maintainers | nepstein |
| Keywords | stochastic, histogram, Markov, probability, Brownian, Normal, Poisson |

## Links

- npm: https://www.npmjs.com/package/stochastic
- Repository: https://github.com/NathanEpstein/stochastic
- Issues: https://github.com/NathanEpstein/stochastic/issues
- npm.io page: https://npm.io/package/stochastic

## Recent versions

- 0.0.14 (latest) — 2015-09-26
- 0.0.13 — 2015-04-29
- 0.0.12 — 2014-12-09
- 0.0.11 — 2014-11-03
- 0.0.10 — 2014-10-22
- 0.0.9 — 2014-10-21
- 0.0.8 — 2014-10-06
- 0.0.7 — 2014-09-25
- 0.0.6 — 2014-09-25
- 0.0.5 — 2014-08-08
- 0.0.4 — 2014-08-08
- 0.0.3 — 2014-08-08
- 0.0.2 — 2014-08-06
- 0.0.1 — 2014-08-06

## README

stochastic
==========

![Geometric Brownian Motion](https://raw.githubusercontent.com/NathanEpstein/stochastic/master/GBM.png)

## Install
`npm install stochastic --save`


## Usage
```javascript
var stoch = require('stochastic');

var normalArray = stoch.norm(mu,sigma,num);

var brownianMotion = stoch.brown(mu, sigma, T, steps, path);

var geometricBrownianMotion = stoch.GBM(S0, mu, sigma, T, steps, path);

var discreteMarkovChain = stoch.DTMC(transMatrix, steps, start, path);

var continuousMarkovChain = stoch.CTMC(transMatrix, T, start, path);

var poissonProcess = stoch.poissP(lambda, T, path);

var sample = stoch.sample(array, num);

var histogram = stoch.hist(array);

var exp = stoch.exp(lambda);

var pareto = stoch.pareto(x_m,alpha);

```

## Extended Usage Notes
### stoch.norm(mu, sigma, num)

Returns an array with num i.i.d normal random variables (http://en.wikipedia.org/wiki/Normal_distribution) of mean mu and standard deviation sigma.

Parameters: mu is a real number, sigma is a strictly positive real number, and num is a positive integer (defaults to 1).

### stoch.brown(mu, sigma, T, steps, path)

Returns an array corresponding to the path of Brownian motion (http://en.wikipedia.org/wiki/Wiener_process#Related_processes) from time 0 to T with drift parameter mu and volatility parameter sigma (the process is initialized to be 0). The i-th entry in the array corresponds to the Brownian process at time i * (T/steps).

Parameters: mu is a real number, sigma is a strictly positive real number, T is a strictly positive real number, steps is a positive integer, and path is a boolean. If path is false, returns only the value of the Brownian process at time T (defaults to true).

### stoch.GBM(S0, mu, sigma, T, steps, path)

Returns an array corresponding to the path of geometric Brownian motion (http://en.wikipedia.org/wiki/Geometric_Brownian_motion) from time 0 to T with drift parameter mu and volatility parameter sigma (the process is initialized to be S0). The i-th entry in the array corresponds to the geometric Brownian process at time i * (T/steps).

Parameters: S0 is a strictly positive real number, mu is a real number, sigma is a strictly positive real number, T is a strictly positive real number, steps is a positive integer, and path is a boolean. If path is false, returns only the value of the geometric Brownian process at time T (defaults to true).

### stoch.DTMC(transMatrix, steps, start, path)

Returns an array with the states at each step of the discrete-time Markov Chain (http://en.wikipedia.org/wiki/Markov_chain) given by transMatrix (2-d array). The number of transitions is given by steps. The initial state is given by start (the states are indexed from 0 to n-1 where n is the number of arrays in transMatrix).

Parameters: transMatrix is a symmetric 2-d array, steps is a positive integer, start is a non-negative integer, and path is a boolean. If path is false, returns only the value of the final state (defaults to true).

### stoch.CTMC(transMatrix, T, start, path)

Returns an object with the {key:value} pair {time:state} at each step of the continuous-time Markov Chain (http://en.wikipedia.org/wiki/Continuous-time_Markov_chain) given by transMatrix (2-d array). The Markov Chain is simulated until time T. The initial state is given by start (the states are indexed from 0 to n-1 where n is the number of arrays in transMatrix).

Parameters: transMatrix is a symmetric 2-d array, T is a strictly positive real number, start is a non-negative integer, and path is a boolean. If path is false, returns only the value of the final state (defaults to true).

### stoch.poissP(lambda, T, path)

Returns an array with the times of each arrival in a Poisson Process (http://en.wikipedia.org/wiki/Poisson_process) with rate lambda until time T.

Parameters: lambda is a strictly positive real number, T is a strictly positive real number, and path is a boolean. If path is false, returns only the number of arrivals (defaults to true).

### stoch.sample(arr, n)

Generates a random sample (with replacement) from a user input array of observations. Number of observations is specified by the user.

Parameters: arr is an array of values and n is a positive integer designating the number of observations.


### stoch.hist(arr)

Generates a histogram object from an array of data. Keys denote the lower bound of each bin and the values indicate the frequency of data in each bin.

Parameters: arr is an array of numeric values.

###stoch.exp(lambda)

Generates an exponential random variable with rate parameter lambda.

Parameters: lambda is a positive real number.

###stoch.pareto(x_m,alpha)

Generates a pareto random variables with paramters x_m and alpha.

Parameters: x_m is a positive real number and alpha is a real number.

## License

**The MIT License (MIT)**

> Copyright (c) 2014 Nathan Epstein
>
> Permission is hereby granted, free of charge, to any person obtaining a copy
> of this software and associated documentation files (the "Software"), to deal
> in the Software without restriction, including without limitation the rights
> to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
> copies of the Software, and to permit persons to whom the Software is
> furnished to do so, subject to the following conditions:
>
> The above copyright notice and this permission notice shall be included in
> all copies or substantial portions of the Software.
>
> THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
> IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
> FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
> AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
> LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
> OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
> THE SOFTWARE.

---
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