# 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
``````