Fisher's F

F distribution constructor.

Usage

var F = require( '@stdlib/math/base/dists/f/ctor' );

F( [d1, d2] )

Returns a F distribution object.

var f = new F();

var mu = f.mean;
// returns NaN

By default, d1 = 1.0 and d2 = 1.0. To create a distribution having a different d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom), provide parameter values.

var f = new F( 2.0, 4.0 );

var mu = f.mean;
// returns 2.0

f

A F distribution object has the following properties and methods...

Writable Properties

f.d1

Numerator degrees of freedom of the distribution. d1 must be a positive number.

var f = new F();

var d1 = f.d1;
// returns 1.0

f.d1 = 3.0;

d1 = f.d1;
// returns 3.0

f.d2

Denominator degrees of freedom of the distribution. d2 must be a positive number.

var f = new F( 2.0, 4.0 );

var d2 = f.d2;
// returns 4.0

f.d2 = 3.0;

d2 = f.d2;
// returns 3.0

Computed Properties

F.prototype.entropy

Returns the differential entropy.

var f = new F( 4.0, 12.0 );

var entropy = f.entropy;
// returns ~1.12

F.prototype.kurtosis

Returns the excess kurtosis.

var f = new F( 4.0, 12.0 );

var kurtosis = f.kurtosis;
// returns ~26.143

F.prototype.mean

Returns the expected value.

var f = new F( 4.0, 12.0 );

var mu = f.mean;
// returns 1.2

F.prototype.mode

Returns the mode.

var f = new F( 4.0, 12.0 );

var mode = f.mode;
// returns ~0.429

F.prototype.skewness

Returns the skewness.

var f = new F( 4.0, 12.0 );

var skewness = f.skewness;
// returns ~3.207

F.prototype.stdev

Returns the standard deviation.

var f = new F( 4.0, 12.0 );

var s = f.stdev;
// returns ~1.122

F.prototype.variance

Returns the variance.

var f = new F( 4.0, 12.0 );

var s2 = f.variance;
// returns 1.26

Methods

F.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var f = new F( 2.0, 4.0 );

var y = f.cdf( 0.5 );
// returns ~0.36

F.prototype.pdf( x )

Evaluates the probability density function (PDF).

var f = new F( 2.0, 4.0 );

var y = f.pdf( 0.8 );
// returns ~0.364

F.prototype.quantile( p )

Evaluates the quantile function at probability p.

var f = new F( 2.0, 4.0 );

var y = f.quantile( 0.5 );
// returns ~0.828

y = quantile( 1.9 );
// returns NaN

Examples

var F = require( '@stdlib/math/base/dists/f/ctor' );

var f = new F( 2.0, 4.0 );

var mu = f.mean;
// returns 1.5

var mode = f.mode;
// returns ~0.45

var s2 = f.variance;
// returns 4.05

var y = f.cdf( 0.8 );
// returns ~0.412