time-to-botec

README.md (9265B)

---

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 # Poisson Random Numbers
 
 > [Poisson][poisson] distributed pseudorandom numbers.
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var poisson = require( '@stdlib/random/base/poisson' );
 ```
 
 #### poisson( lambda )
 
 Returns a pseudorandom number drawn from a [Poisson][poisson] distribution with mean parameter `lambda`.
 
 ```javascript
 var r = poisson( 7.9 );
 // returns <number>
 ```
 
 If `lambda <= 0` or `lambda` is `NaN`, the function returns `NaN`.
 
 ```javascript
 var r = poisson( -2.0 );
 // returns NaN
 
 r = poisson( NaN );
 // returns NaN
 ```
 
 #### poisson.factory( \[lambda, ]\[options] )
 
 Returns a pseudorandom number generator (PRNG) for generating pseudorandom numbers drawn from a [Poisson][poisson] distribution.
 
 ```javascript
 var rand = poisson.factory();
 
 var r = rand( 15.0 );
 // returns <number>
 ```
 
 If provided `lambda`, the returned generator returns random variates from the specified distribution.
 
 ```javascript
 var rand = poisson.factory( 10.0 );
 
 var r = rand();
 // returns <number>
 
 r = rand();
 // returns <number>
 ```
 
 If not provided `lambda`, the returned generator requires that `lambda` be provided at each invocation.
 
 ```javascript
 var rand = poisson.factory();
 
 var r = rand( 4.0 );
 // returns <number>
 
 r = rand( 3.14 );
 // returns <number>
 ```
 
 The function accepts the following `options`:
 
 -   **prng**: pseudorandom number generator for generating uniformly distributed pseudorandom numbers on the interval `[0,1)`. If provided, the function **ignores** both the `state` and `seed` options. In order to seed the returned pseudorandom number generator, one must seed the provided `prng` (assuming the provided `prng` is seedable).
 -   **seed**: pseudorandom number generator seed.
 -   **state**: a [`Uint32Array`][@stdlib/array/uint32] containing pseudorandom number generator state. If provided, the function ignores the `seed` option.
 -   **copy**: `boolean` indicating whether to copy a provided pseudorandom number generator state. Setting this option to `false` allows sharing state between two or more pseudorandom number generators. Setting this option to `true` ensures that a returned generator has exclusive control over its internal state. Default: `true`.
 
 To use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the `prng` option.
 
 ```javascript
 var minstd = require( '@stdlib/random/base/minstd' );
 
 var rand = poisson.factory({
     'prng': minstd.normalized
 });
 
 var r = rand( 3.0 );
 // returns <number>
 ```
 
 To seed a pseudorandom number generator, set the `seed` option.
 
 ```javascript
 var rand1 = poisson.factory({
     'seed': 12345
 });
 
 var r1 = rand1( 3.0 );
 // returns <number>
 
 var rand2 = poisson.factory( 3.0, {
     'seed': 12345
 });
 
 var r2 = rand2();
 // returns <number>
 
 var bool = ( r1 === r2 );
 // returns true
 ```
 
 To return a generator having a specific initial state, set the generator `state` option.
 
 ```javascript
 var rand;
 var bool;
 var r;
 var i;
 
 // Generate pseudorandom numbers, thus progressing the generator state:
 for ( i = 0; i < 1000; i++ ) {
     r = poisson( 10.0 );
 }
 
 // Create a new PRNG initialized to the current state of `poisson`:
 rand = poisson.factory({
     'state': poisson.state
 });
 
 // Test that the generated pseudorandom numbers are the same:
 bool = ( rand( 10.0 ) === poisson( 10.0 ) );
 // returns true
 ```
 
 #### poisson.NAME
 
 The generator name.
 
 ```javascript
 var str = poisson.NAME;
 // returns 'poisson'
 ```
 
 #### poisson.PRNG
 
 The underlying pseudorandom number generator.
 
 ```javascript
 var prng = poisson.PRNG;
 // returns <Function>
 ```
 
 #### poisson.seed
 
 The value used to seed `poisson()`.
 
 ```javascript
 var rand;
 var r;
 var i;
 
 // Generate pseudorandom values...
 for ( i = 0; i < 100; i++ ) {
     r = poisson( 2.0 );
 }
 
 // Generate the same pseudorandom values...
 rand = poisson.factory( 2.0, {
     'seed': poisson.seed
 });
 for ( i = 0; i < 100; i++ ) {
     r = rand();
 }
 ```
 
 If provided a PRNG for uniformly distributed numbers, this value is `null`.
 
 <!-- eslint-disable stdlib/no-builtin-math -->
 
 ```javascript
 var rand = poisson.factory({
     'prng': Math.random
 });
 
 var seed = rand.seed;
 // returns null
 ```
 
 #### poisson.seedLength
 
 Length of generator seed.
 
 ```javascript
 var len = poisson.seedLength;
 // returns <number>
 ```
 
 If provided a PRNG for uniformly distributed numbers, this value is `null`.
 
 <!-- eslint-disable stdlib/no-builtin-math -->
 
 ```javascript
 var rand = poisson.factory({
     'prng': Math.random
 });
 
 var len = rand.seedLength;
 // returns null
 ```
 
 #### poisson.state
 
 Writable property for getting and setting the generator state.
 
 ```javascript
 var r = poisson( 10.0 );
 // returns <number>
 
 r = poisson( 10.0 );
 // returns <number>
 
 // ...
 
 // Get a copy of the current state:
 var state = poisson.state;
 // returns <Uint32Array>
 
 r = poisson( 10.0 );
 // returns <number>
 
 r = poisson( 10.0 );
 // returns <number>
 
 // Reset the state:
 poisson.state = state;
 
 // Replay the last two pseudorandom numbers:
 r = poisson( 10.0 );
 // returns <number>
 
 r = poisson( 10.0 );
 // returns <number>
 
 // ...
 ```
 
 If provided a PRNG for uniformly distributed numbers, this value is `null`.
 
 <!-- eslint-disable stdlib/no-builtin-math -->
 
 ```javascript
 var rand = poisson.factory({
     'prng': Math.random
 });
 
 var state = rand.state;
 // returns null
 ```
 
 #### poisson.stateLength
 
 Length of generator state.
 
 ```javascript
 var len = poisson.stateLength;
 // returns <number>
 ```
 
 If provided a PRNG for uniformly distributed numbers, this value is `null`.
 
 <!-- eslint-disable stdlib/no-builtin-math -->
 
 ```javascript
 var rand = poisson.factory({
     'prng': Math.random
 });
 
 var len = rand.stateLength;
 // returns null
 ```
 
 #### poisson.byteLength
 
 Size (in bytes) of generator state.
 
 ```javascript
 var sz = poisson.byteLength;
 // returns <number>
 ```
 
 If provided a PRNG for uniformly distributed numbers, this value is `null`.
 
 <!-- eslint-disable stdlib/no-builtin-math -->
 
 ```javascript
 var rand = poisson.factory({
     'prng': Math.random
 });
 
 var sz = rand.byteLength;
 // returns null
 ```
 
 #### poisson.toJSON()
 
 Serializes the pseudorandom number generator as a JSON object.
 
 ```javascript
 var o = poisson.toJSON();
 // returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }
 ```
 
 If provided a PRNG for uniformly distributed numbers, this method returns `null`.
 
 <!-- eslint-disable stdlib/no-builtin-math -->
 
 ```javascript
 var rand = poisson.factory({
     'prng': Math.random
 });
 
 var o = rand.toJSON();
 // returns null
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   If PRNG state is "shared" (meaning a state array was provided during PRNG creation and **not** copied) and one sets the generator state to a state array having a different length, the PRNG does **not** update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for **each** relevant PRNG must be **explicitly** set.
 -   If PRNG state is "shared" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).
 
 </section>
 
 <!-- /.notes -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var poisson = require( '@stdlib/random/base/poisson' );
 
 var seed;
 var rand;
 var i;
 
 // Generate pseudorandom numbers...
 for ( i = 0; i < 100; i++ ) {
     console.log( poisson( 8.0 ) );
 }
 
 // Create a new pseudorandom number generator...
 seed = 1234;
 rand = poisson.factory( 0.8, {
     'seed': seed
 });
 for ( i = 0; i < 100; i++ ) {
     console.log( rand() );
 }
 
 // Create another pseudorandom number generator using a previous seed...
 rand = poisson.factory( 8.0, {
     'seed': poisson.seed
 });
 for ( i = 0; i < 100; i++ ) {
     console.log( rand() );
 }
 ```
 
 </section>
 
 <!-- /.examples -->
 
 * * *
 
 <section class="references">
 
 ## References
 
 -   Knuth, Donald E. 1997. _The Art of Computer Programming, Volume 2 (3rd Ed.): Seminumerical Algorithms_. Boston, MA, USA: Addison-Wesley Longman Publishing Co., Inc.
 -   Hörmann, W. 1993. "The transformed rejection method for generating Poisson random variables." _Insurance: Mathematics and Economics_ 12 (1): 39–45. doi:[10.1016/0167-6687(93)90997-4][@hormann:1993b].
 
 </section>
 
 <!-- /.references -->
 
 <section class="links">
 
 [poisson]: https://en.wikipedia.org/wiki/Poisson_distribution
 
 [@hormann:1993b]: http://dx.doi.org/10.1016/0167-6687(93)90997-4
 
 [@stdlib/array/uint32]: https://www.npmjs.com/package/@stdlib/array-uint32
 
 </section>
 
 <!-- /.links -->