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Kernel Betaincinv

Inverse of the lower incomplete beta function.

The function computes the inverse of the lower regularized incomplete beta function. This is a kernel function used internally by higher-level inverse beta function implementations.

Installation

npm install @stdlib/math-base-special-kernel-betaincinv

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var kernelBetaincinv = require( '@stdlib/math-base-special-kernel-betaincinv' );

kernelBetaincinv( a, b, p, q )

Inverts the lower regularized incomplete beta function at a > 0 and b > 0. Input probabilities p and q must satisfy p = 1 - q. The function returns a two-element array holding the function value y and 1-y.

var y = kernelBetaincinv( 3.0, 3.0, 0.2, 0.8 );
// returns [ ~0.327, ~0.673 ]

y = kernelBetaincinv( 3.0, 3.0, 0.4, 0.6 );
// returns [ ~0.446, ~0.554 ]

y = kernelBetaincinv( 1.0, 6.0, 0.4, 0.6 );
// returns [ ~0.082, ~0.918 ]

y = kernelBetaincinv( 1.0, 6.0, 0.8, 0.2 );
// returns [ ~0.235, ~0.765 ]

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var kernelBetaincinv = require( '@stdlib/math-base-special-kernel-betaincinv' );

var out;
var i;
var p;
var a;
var b;

for ( i = 0; i < 100; i++ ) {
    p = randu();
    a = ( randu() * 10.0 ) + EPS;
    b = ( randu() * 10.0 ) + EPS;
    out = kernelBetaincinv( a, b, p, 1.0-p );
    console.log( 'p: %d, \t a: %d, \t b: %d, \t y: %d, \t 1-y: %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) );
}

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C APIs

Usage

#include "stdlib/math/base/special/kernel_betaincinv.h"

stdlib_base_kernel_betaincinv( a, b, p, q, &out1, &out2 )

Computes the inverse of the lower incomplete beta function.

double out1;
double out2;

stdlib_base_kernel_betaincinv( 3.0, 3.0, 0.2, 0.8, &out1, &out2 );

The function accepts the following arguments:

• a: [in] double first function parameter (a positive number).
• b: [in] double second function parameter (a positive number).
• p: [in] double probability.
• q: [in] double probability equal to 1-p.
• out1: [out] double* destination pointer to store the function value y.
• out2: [out] double* destination pointer to store 1-y.

void stdlib_base_kernel_betaincinv( const double a, const double b, const double p, const double q, double *out1, double *out2 );

Examples

#include "stdlib/math/base/special/kernel_betaincinv.h"
#include "stdlib/constants/float64/eps.h"
#include "stdlib/random/base/randu.h"
#include <stdio.h>
#include <stdint.h>

int main( void ) {
    struct BasePRNGObject *obj = stdlib_base_random_randu_allocate( 0 );
    double out1;
    double out2;
    int32_t i;
    double p;
    double a;
    double b;

    for ( i = 0; i < 100; i++ ) {
        p = stdlib_base_random_randu( obj );
        a = ( stdlib_base_random_randu( obj ) * 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
        b = ( stdlib_base_random_randu( obj ) * 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
        stdlib_base_kernel_betaincinv( a, b, p, 1.0-p, &out1, &out2 );
        printf( "p: %lf, a: %lf, b: %lf, y: %lf, 1-y: %lf\n", p, a, b, out1, out2 );
    }

    stdlib_base_random_randu_free( obj );
}

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See Also

• @stdlib/math-base/special/betaincinv: inverse incomplete beta function.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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Copyright

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