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Pareto (Type I) distribution constructor.
npm install @stdlib/stats-base-dists-pareto-type1-ctor
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var Pareto1 = require( '@stdlib/stats-base-dists-pareto-type1-ctor' );
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
A Pareto (Type I) distribution object has the following properties and methods...
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
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
Returns the differential entropy.
var pareto1 = new Pareto1( 4.0, 12.0 );
var entropy = pareto1.entropy;
// returns ~2.349
Returns the excess kurtosis.
var pareto1 = new Pareto1( 6.0, 12.0 );
var kurtosis = pareto1.kurtosis;
// returns ~35.667
Returns the expected value.
var pareto1 = new Pareto1( 4.0, 12.0 );
var mu = pareto1.mean;
// returns 16.0
Returns the median.
var pareto1 = new Pareto1( 4.0, 12.0 );
var median = pareto1.median;
// returns ~14.27
Returns the mode.
var pareto1 = new Pareto1( 4.0, 12.0 );
var mode = pareto1.mode;
// returns 12.0
Returns the skewness.
var pareto1 = new Pareto1( 4.0, 12.0 );
var skewness = pareto1.skewness;
// returns ~7.071
Returns the variance.
var pareto1 = new Pareto1( 4.0, 12.0 );
var s2 = pareto1.variance;
// returns 32.0
Evaluates the cumulative distribution function (CDF).
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.cdf( 3.5 );
// returns 0.0
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
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
Evaluates the probability density function (PDF).
var pareto1 = new Pareto1( 2.0, 4.0 );
var y = pareto1.pdf( 5.0 );
// returns ~0.256
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
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
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