Student's T

Student's t distribution constructor.

Usage

var T = require( '@stdlib/math/base/dists/t/ctor' );

T( [v] )

Returns a Student's t distribution object.

var t = new T();

var mu = t.mean;
// returns NaN

By default, v = 1.0. To create a distribution having a different degrees of freedom v, provide a parameter value.

var t = new T( 4.0 );

var mu = t.mean;
// returns 0.0

t

A Student's t distribution object has the following properties and methods...

Writable Properties

t.v

Degrees of freedom of the distribution. v must be a positive number.

var t = new T( 2.0 );

var v = t.v;
// returns 2.0

t.v = 3.0;

v = t.v;
// returns 3.0

Computed Properties

T.prototype.entropy

Returns the differential entropy.

var t = new T( 4.0 );

var entropy = t.entropy;
// returns ~1.682

T.prototype.kurtosis

Returns the excess kurtosis.

var t = new T( 4.0 );

var kurtosis = t.kurtosis;
// returns Infinity

T.prototype.mean

Returns the expected value.

var t = new T( 4.0 );

var mu = t.mean;
// returns 0.0

T.prototype.median

Returns the median.

var t = new T( 4.0 );

var median = t.median;
// returns 0.0

T.prototype.mode

Returns the mode.

var t = new T( 4.0 );

var mode = t.mode;
// returns 0.0

T.prototype.skewness

Returns the skewness.

var t = new T( 4.0 );

var skewness = t.skewness;
// returns 0.0

T.prototype.stdev

Returns the standard deviation.

var t = new T( 4.0 );

var s = t.stdev;
// returns ~1.414

T.prototype.variance

Returns the variance.

var t = new T( 4.0 );

var s2 = t.variance;
// returns 2.0

Methods

T.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var t = new T( 2.0 );

var y = t.cdf( 0.5 );
// returns ~0.667

T.prototype.logcdf( x )

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

var t = new T( 2.0 );

var y = t.logcdf( 0.5 );
// returns ~-0.405

T.prototype.logpdf( x )

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

var t = new T( 2.0 );

var y = t.logpdf( 0.8 );
// returns ~-1.457

T.prototype.pdf( x )

Evaluates the probability density function (PDF).

var t = new T( 2.0 );

var y = t.pdf( 0.8 );
// returns ~0.233

T.prototype.quantile( p )

Evaluates the quantile function at probability p.

var t = new T( 2.0 );

var y = t.quantile( 0.5 );
// returns 0.0

y = quantile( 1.9 );
// returns NaN

Examples

var T = require( '@stdlib/math/base/dists/t/ctor' );

var t = new T( 2.0 );

var mu = t.mean;
// returns 0.0

var mode = t.mode;
// returns 0.0

var s2 = t.variance;
// returns Infinity

var y = t.cdf( 0.8 );
// returns ~0.746