Fréchet
Fréchet distribution constructor.
Usage
var Frechet = require( '@stdlib/stats/base/dists/frechet/ctor' );
Frechet( [alpha, s, m] )
Returns a Fréchet distribution object.
var frechet = new Frechet();
var mu = frechet.mean;
// returns Infinity
By default, alpha = 1.0
, s = 1.0
, and m = 0.0
. To create a distribution having a different alpha
(shape), s
(scale), and m
(location), provide the corresponding arguments.
var frechet = new Frechet( 2.0, 4.0, 3.5 );
var mu = frechet.mean;
// returns ~10.59
frechet
An Fréchet distribution object has the following properties and methods...
Writable Properties
frechet.alpha
Shape parameter of the distribution. alpha
must be a positive number.
var frechet = new Frechet();
var alpha = frechet.alpha;
// returns 1.0
frechet.alpha = 0.5;
alpha = frechet.alpha;
// returns 0.5
frechet.s
Scale parameter of the distribution. s
must be a positive number.
var frechet = new Frechet( 2.0, 4.0, 1.5 );
var s = frechet.s;
// returns 4.0
frechet.s = 3.0;
s = frechet.s;
// returns 3.0
frechet.m
Location parameter of the distribution.
var frechet = new Frechet( 2.0, 2.0, 4.0 );
var m = frechet.m;
// returns 4.0
frechet.m = 3.0;
m = frechet.m;
// returns 3.0
Computed Properties
Frechet.prototype.entropy
Returns the differential entropy.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var entropy = frechet.entropy;
// returns ~2.82
Frechet.prototype.kurtosis
Returns the excess kurtosis.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var kurtosis = frechet.kurtosis;
// returns Infinity
Frechet.prototype.mean
Returns the expected value.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var mu = frechet.mean;
// returns ~16.705
Frechet.prototype.median
Returns the median.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var median = frechet.median;
// returns ~15.151
Frechet.prototype.mode
Returns the mode.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var mode = frechet.mode;
// returns ~13.349
Frechet.prototype.skewness
Returns the skewness.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var skewness = frechet.skewness;
// returns ~5.605
Frechet.prototype.stdev
Returns the standard deviation.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var s = frechet.stdev;
// returns ~6.245
Frechet.prototype.variance
Returns the variance.
var frechet = new Frechet( 4.0, 12.0, 2.0 );
var s2 = frechet.variance;
// returns ~38.996
Methods
Frechet.prototype.cdf( x )
Evaluates the cumulative distribution function (CDF).
var frechet = new Frechet( 2.0, 4.0, 3.0 );
var y = frechet.cdf( 2.5 );
// returns 0.0
Frechet.prototype.logcdf( x )
Evaluates the natural logarithm of the cumulative distribution function (CDF).
var frechet = new Frechet( 2.0, 4.0, 3.0 );
var y = frechet.logcdf( 2.5 );
// returns -Infinity
Frechet.prototype.logpdf( x )
Evaluates the natural logarithm of the probability density function (PDF).
var frechet = new Frechet( 2.0, 4.0, 3.0 );
var y = frechet.logpdf( 5.5 );
// returns ~-1.843
Frechet.prototype.pdf( x )
Evaluates the probability density function (PDF).
var frechet = new Frechet( 2.0, 4.0, 3.0 );
var y = frechet.pdf( 5.5 );
// returns ~0.158
Frechet.prototype.quantile( p )
Evaluates the quantile function at probability p
.
var frechet = new Frechet( 2.0, 4.0, 3.0 );
var y = frechet.quantile( 0.5 );
// returns ~7.804
y = frechet.quantile( 1.9 );
// returns NaN
Examples
var Frechet = require( '@stdlib/stats/base/dists/frechet/ctor' );
var frechet = new Frechet( 2.0, 4.0, 3.0 );
var mu = frechet.mean;
// returns ~10.09
var median = frechet.median;
// returns ~7.804
var s2 = frechet.variance;
// returns Infinity
var y = frechet.cdf( 2.5 );
// returns 0.0