Beta prime distribution mode.
APACHE-2.0 License
Beta prime distribution mode.
The mode for a beta prime random variable is
\mathop{\mathrm{mode}}(X) = \begin{cases}\frac{\alpha-1}{\beta+1} & \text{ if } \alpha \ge 1 \\ 0 & \text{ otherwise }\end{cases}
where α > 0
is the first shape parameter and β > 0
is the second shape parameter.
npm install @stdlib/stats-base-dists-betaprime-mode
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).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.
var mode = require( '@stdlib/stats-base-dists-betaprime-mode' );
Returns the mode of a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var v = mode( 8.0, 2.0 );
// returns ~2.333
v = mode( 4.0, 12.0 );
// returns ~0.231
v = mode( 1.0, 2.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var v = mode( NaN, 2.0 );
// returns NaN
v = mode( 2.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var v = mode( 0.0, 1.0 );
// returns NaN
v = mode( -1.0, 1.0 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var v = mode( 1.0, 0.0 );
// returns NaN
v = mode( 1.0, -1.0 );
// returns NaN
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var mode = require( '@stdlib/stats-base-dists-betaprime-mode' );
var alpha;
var beta;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*10.0 ) + EPS;
beta = ( randu()*10.0 ) + EPS;
v = mode( alpha, beta );
console.log( 'α: %d, β: %d, mode(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}
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.
See LICENSE.
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