@stdlib/stats/base/dists/negative-binomial/mean/README.md

Standard library statistical functions.

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# Mean

> [Negative binomial][negative-binomial-distribution] distribution [expected value][expected-value].

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The [mean][expected-value] for a [negative binomial][negative-binomial-distribution] random variable is

<!-- <equation class="equation" label="eq:negative_binomial_mean" align="center" raw="\mathbb{E} \left[ X \right] = \frac{pr}{1-p}" alt="Mean for a negative binomial distribution."> -->

<div class="equation" align="center" data-raw-text="\mathbb{E} \left[ X \right] = \frac{pr}{1-p}" data-equation="eq:negative_binomial_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/mean/docs/img/equation_negative_binomial_mean.svg" alt="Mean for a negative binomial distribution.">
    <br>
</div>

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where `r` is the number of successes until experiment is stopped and `p` is the success probability in each trial. The random variable `X` denotes the number of failures until the `r` success is reached. 

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## Usage

```javascript
var mean = require( '@stdlib/stats/base/dists/negative-binomial/mean' );
```

#### mean( r, p )

Returns the [expected value][expected-value] of a [negative binomial][negative-binomial-distribution] distribution with parameters `r` (number of successes until experiment is stopped) and `p` (success probability).

```javascript
var v = mean( 100, 0.2 );
// returns 400

v = mean( 50, 0.5 );
// returns 50
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var v = mean( NaN, 0.5 );
// returns NaN

v = mean( 20, NaN );
// returns NaN
```

If provided a `r` which is not a positive number, the function returns `NaN`.

```javascript
var v = mean( -2.0, 0.5 );
// returns NaN
```

If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.

```javascript
var v = mean( 20, -1.0 );
// returns NaN

v = mean( 20, 1.5 );
// returns NaN
```

</section>

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</section>

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## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var mean = require( '@stdlib/stats/base/dists/negative-binomial/mean' );

var v;
var i;
var r;
var p;

for ( i = 0; i < 10; i++ ) {
    r = randu() * 100;
    p = randu();
    v = mean( r, p );
    console.log( 'r: %d, p: %d, E(X;r,p): %d', r, p.toFixed( 4 ), v.toFixed( 4 ) );
}
```

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</section>

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[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

</section>

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