time-to-botec

README.md (5010B)

---

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 # Logarithm of Probability Mass Function
 
 > Evaluate the natural logarithm of the [probability mass function][pmf] (PMF) for a [negative binomial][negative-binomial-distribution] distribution.
 
 <section class="intro">
 
 The [probability mass function][pmf] (PMF) for a [negative binomial][negative-binomial-distribution] random variable `X` is
 
 <!-- <equation class="equation" label="eq:negative_binomial_pmf" align="center" raw="f(x; r, p) = P(X = x; r,p) = \binom{k+r-1}{x} p^r(1-p)^x \quad\text{for }x = 0, 1, 2, \dotsc" alt="Probability mass function (PMF) for a negative binomial distribution."> -->
 
 <div class="equation" align="center" data-raw-text="f(x; r, p) = P(X = x; r,p) = \binom{k+r-1}{x} p^r(1-p)^x \quad\text{for }x = 0, 1, 2, \dotsc" data-equation="eq:negative_binomial_pmf">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/logpmf/docs/img/equation_negative_binomial_pmf.svg" alt="Probability mass function (PMF) for a negative binomial distribution.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 where `r > 0` is the number of successes until experiment is stopped and `0 < p <= 1` is the success probability. The random variable `X` denotes the number of failures until the `r` success is reached. 
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var logpmf = require( '@stdlib/stats/base/dists/negative-binomial/logpmf' );
 ```
 
 #### logpmf( x, r, p )
 
 Evaluates the natural logarithm of the [probability mass function][pmf] for a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped `r` and success probability `p`.
 
 ```javascript
 var y = logpmf( 5.0, 20.0, 0.8 );
 // returns ~-1.853
 
 y = logpmf( 21.0, 20.0, 0.5 );
 // returns ~-2.818
 
 y = logpmf( 5.0, 10.0, 0.4 );
 // returns ~-4.115
 
 y = logpmf( 0.0, 10.0, 0.9 );
 // returns ~-1.054
 ```
 
 While `r` can be interpreted as the number of successes until the experiment is stopped, the [negative binomial][negative-binomial-distribution] distribution is also defined for non-integers `r`. In this case, `r` denotes shape parameter of the [gamma mixing distribution][negative-binomial-mixture-representation].
 
 ```javascript
 var y = logpmf( 21.0, 15.5, 0.5 );
 // returns ~-3.292
 
 y = logpmf( 5.0, 7.4, 0.4 );
 // returns ~-2.976
 ```
 
 If provided a `r` which is not a positive number, the function returns `NaN`.
 
 ```javascript
 var y = logpmf( 2.0, 0.0, 0.5 );
 // returns NaN
 
 y = logpmf( 2.0, -2.0, 0.5 );
 // returns NaN
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.
 
 ```javascript
 var y = logpmf( NaN, 20.0, 0.5 );
 // returns NaN
 
 y = logpmf( 0.0, NaN, 0.5 );
 // returns NaN
 
 y = logpmf( 0.0, 20.0, NaN );
 // returns NaN
 ```
 
 If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.
 
 ```javascript
 var y = logpmf( 2.0, 20, -1.0 );
 // returns NaN
 
 y = logpmf( 2.0, 20, 1.5 );
 // returns NaN
 ```
 
 #### logpmf.factory( r, p )
 
 Returns a function for evaluating the natural logarithm of the [probability mass function][pmf] (PMF) of a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped `r` and success probability `p`.
 
 ```javascript
 var mylogpmf = logpmf.factory( 10, 0.5 );
 var y = mylogpmf( 3.0 );
 // returns ~-3.617
 
 y = mylogpmf( 10.0 );
 // returns ~-2.43
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var randu = require( '@stdlib/random/base/randu' );
 var round = require( '@stdlib/math/base/special/round' );
 var logpmf = require( '@stdlib/stats/base/dists/negative-binomial/logpmf' );
 
 var i;
 var r;
 var p;
 var x;
 var y;
 
 for ( i = 0; i < 10; i++ ) {
     x = round( randu() * 30.0 );
     r = randu() * 50.0;
     p = randu();
     y = logpmf( x, r, p );
     console.log( 'x: %d, r: %d, p: %d, ln(P(X=x;r,p)): %d', x, r, p.toFixed( 4 ), y.toFixed( 4 ) );
 }
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [negative-binomial-mixture-representation]: https://en.wikipedia.org/wiki/Negative_binomial_distribution#Gamma.E2.80.93Poisson_mixture
 
 [negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution
 
 [pmf]: https://en.wikipedia.org/wiki/Probability_mass_function
 
 </section>
 
 <!-- /.links -->