# betaincinv
> Inverse of the [incomplete beta function][incomplete-beta-function].
## Usage
```javascript
var betaincinv = require( '@stdlib/math/base/special/betaincinv' );
```
#### betaincinv( p, a, b\[, upper] )
Inverts the regularized [incomplete beta function][incomplete-beta-function]. Contrary to the more commonly used definition, in this implementation the first parameter is the probability `p` and the second and third parameter are `a` and `b`. By default, the function inverts the _lower_ regularized [incomplete beta function][incomplete-beta-function]. To invert the _upper_ function instead, set the `upper` argument to `true`.
```javascript
var y = betaincinv( 0.2, 3.0, 3.0 );
// returns ~0.327
y = betaincinv( 0.4, 3.0, 3.0 );
// returns ~0.446
y = betaincinv( 0.4, 3.0, 3.0, true );
// returns ~0.554
y = betaincinv( 0.4, 1.0, 6.0 );
// returns ~0.082
y = betaincinv( 0.8, 1.0, 6.0 );
// returns ~0.235
```
If provided `NaN` as any argument, the function returns `NaN`.
```javascript
var y = betaincinv( NaN, 1.0, 1.0 );
// returns NaN
y = betaincinv( 0.5, NaN, 1.0 );
// returns NaN
y = betaincinv( 0.5, 1.0, NaN );
// returns NaN
```
If provided a value outside `[0,1]` for `p`, the function returns `NaN`.
```javascript
var y = betaincinv( 1.2, 1.0, 1.0 );
// returns NaN
y = betaincinv( -0.5, 1.0, 1.0 );
// returns NaN
```
If provided a nonpositive `a`, the function returns `NaN`.
```javascript
var y = betaincinv( 0.5, -2.0, 2.0 );
// returns NaN
y = betaincinv( 0.5, 0.0, 2.0 );
// returns NaN
```
If provided a nonpositive `b`, the function returns `NaN`.
```javascript
var y = betaincinv( 0.5, 2.0, -2.0 );
// returns NaN
y = betaincinv( 0.5, 2.0, 0.0 );
// returns NaN
```
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var betaincinv = require( '@stdlib/math/base/special/betaincinv' );
var i;
var p;
var a;
var b;
for ( i = 0; i < 100; i++ ) {
p = randu();
a = randu() * 10.0;
b = randu() * 10.0;
console.log( 'p: %d, \t a: %d, \t b: %d, \t f(p,a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), betaincinv( p, a, b ) );
}
```
[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function