Pareto (Type I)
Pareto (Type I) distribution constructor.
Usage
var Pareto1 = require( '@stdlib/stats/base/dists/pareto-type1/ctor' );
Pareto1( [alpha, beta] )
Returns a Pareto (Type I) distribution object.
var pareto1 = new Pareto1();
var mu = pareto1.mean;
// returns Infinity
By default, alpha = 1.0
and beta = 1.0
. To create a distribution having a different alpha
(shape parameter) and beta
(scale parameter), provide the corresponding arguments.
var pareto1 = new Pareto1( 2.0, 4.0 );
var mu = pareto1.mean;
// returns 8.0
pareto1
A Pareto (Type I) distribution object has the following properties and methods...
Writable Properties
pareto1.alpha
Shape parameter of the distribution. alpha
must be a positive number.
var pareto1 = new Pareto1();
var alpha = pareto1.alpha;
// returns 1.0
pareto1.alpha = 3.0;
alpha = pareto1.alpha;
// returns 3.0
pareto1.beta
Scale parameter of the distribution. beta
must be a positive number.
var pareto1 = new Pareto1( 2.0, 4.0 );
var beta = pareto1.beta;
// returns 4.0
pareto1.beta = 3.0;
beta = pareto1.beta;
// returns 3.0
Computed Properties
Pareto1.prototype.entropy
Returns the differential entropy.
var pareto1 = new Pareto1( 4.0, 12.0 );
var entropy = pareto1.entropy;
// returns ~2.349
Pareto1.prototype.kurtosis
Returns the excess kurtosis.
var pareto1 = new Pareto1( 6.0, 12.0 );
var kurtosis = pareto1.kurtosis;
// returns ~35.667
Pareto1.prototype.mean
Returns the expected value.
var pareto1 = new Pareto1( 4.0, 12.0 );
var mu = pareto1.mean;
// returns 16.0
Pareto1.prototype.median
Returns the median.
var pareto1 = new Pareto1( 4.0, 12.0 );
var median = pareto1.median;
// returns ~14.27
Pareto1.prototype.mode
Returns the mode.
var pareto1 = new Pareto1( 4.0, 12.0 );
var mode = pareto1.mode;
// returns 12.0
Pareto1.prototype.skewness
Returns the skewness.
var pareto1 = new Pareto1( 4.0, 12.0 );
var skewness = pareto1.skewness;
// returns ~7.071
Pareto1.prototype.variance
Returns the variance.
var pareto1 = new Pareto1( 4.0, 12.0 );
var s2 = pareto1.variance;
// returns 32.0
Methods
Pareto1.prototype.cdf( x )
Evaluates the cumulative distribution function (CDF).
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.cdf( 3.5 );
// returns 0.0
Pareto1.prototype.logcdf( x )
Evaluates the natural logarithm of the cumulative distribution function (CDF).
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.logcdf( 3.5 );
// returns -Infinity
Pareto1.prototype.logpdf( x )
Evaluates the natural logarithm of the probability density function (PDF).
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.logpdf( 5.0 );
// returns ~-1.363
Pareto1.prototype.pdf( x )
Evaluates the probability density function (PDF).
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.pdf( 5.0 );
// returns ~0.256
Pareto1.prototype.quantile( p )
Evaluates the quantile function at probability p
.
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.quantile( 0.5 );
// returns ~5.657
y = pareto1.quantile( 1.9 );
// returns NaN
Examples
var Pareto1 = require( '@stdlib/stats/base/dists/pareto-type1/ctor' );
var pareto1 = new Pareto1( 2.0, 4.0 );
var mu = pareto1.mean;
// returns 8.0
var median = pareto1.median;
// returns ~5.657
var s2 = pareto1.variance;
// returns Infinity
var y = pareto1.cdf( 2.0 );
// returns 0.0