Arcsine

Arcsine distribution constructor.

Usage

var Arcsine = require( '@stdlib/math/base/dists/arcsine/ctor' );

Arcsine( [a, b] )

Returns an arcsine distribution object.

var arcsine = new Arcsine();

var mu = arcsine.mean;
// returns 0.5

By default, a = 0.0 and b = 1.0. To create a distribution having a different a (minimum support) and b (maximum support), provide parameter values.

var arcsine = new Arcsine( 2.0, 4.0 );

var mu = arcsine.mean;
// returns 3.0

arcsine

An arcsine distribution object has the following properties and methods...

Writable Properties

arcsine.a

Minimum support of the distribution. a must be a number smaller than b.

var arcsine = new Arcsine();

var a = arcsine.a;
// returns 0.0

arcsine.a = 0.5;

a = arcsine.a;
// returns 0.5

arcsine.b

Maximum support of the distribution. b must be a number larger than a.

var arcsine = new Arcsine( 2.0, 4.0 );

var b = arcsine.b;
// returns 4.0

arcsine.b = 3.0;

b = arcsine.b;
// returns 3.0

Computed Properties

Arcsine.prototype.entropy

Returns the differential entropy.

var arcsine = new Arcsine( 4.0, 12.0 );

var entropy = arcsine.entropy;
// returns ~1.838

Arcsine.prototype.kurtosis

Returns the excess kurtosis.

var arcsine = new Arcsine( 4.0, 12.0 );

var kurtosis = arcsine.kurtosis;
// returns -1.5

Arcsine.prototype.mean

Returns the expected value.

var arcsine = new Arcsine( 4.0, 12.0 );

var mu = arcsine.mean;
// returns 8.0

Arcsine.prototype.median

Returns the median.

var arcsine = new Arcsine( 4.0, 12.0 );

var median = arcsine.median;
// returns 8.0

Arcsine.prototype.mode

Returns the mode.

var arcsine = new Arcsine( 4.0, 12.0 );

var mode = arcsine.mode;
// returns 4.0

Arcsine.prototype.skewness

Returns the skewness.

var arcsine = new Arcsine( 4.0, 12.0 );

var skewness = arcsine.skewness;
// returns 0.0

Arcsine.prototype.stdev

Returns the standard deviation.

var arcsine = new Arcsine( 4.0, 12.0 );

var s = arcsine.stdev;
// returns ~2.828

Arcsine.prototype.variance

Returns the variance.

var arcsine = new Arcsine( 4.0, 12.0 );

var s2 = arcsine.variance;
// returns 8.0

Methods

Arcsine.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.cdf( 2.5 );
// returns ~0.333

Arcsine.prototype.logcdf( x )

Evaluates the natural logarithm of the cumulative distribution function (CDF).

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.logcdf( 2.5 );
// returns ~-1.1

Arcsine.prototype.logpdf( x )

Evaluates the natural logarithm of the probability density function (PDF).

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.logpdf( 2.5 );
// returns ~-1.0

Arcsine.prototype.pdf( x )

Evaluates the probability density function (PDF).

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.pdf( 2.5 );
// returns ~0.368

Arcsine.prototype.quantile( p )

Evaluates the quantile function at probability p.

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.quantile( 0.5 );
// returns 3.0

y = quantile( 1.9 );
// returns NaN

Examples

var Arcsine = require( '@stdlib/math/base/dists/arcsine/ctor' );

var arcsine = new Arcsine( 2.0, 4.0 );

var mu = arcsine.mean;
// returns 3.0

var median = arcsine.median;
// returns 3.0

var s2 = arcsine.variance;
// returns 0.5

var y = arcsine.cdf( 2.5 );
// returns ~0.333