# Pareto (Type I)

Pareto (Type I) distribution constructor.

## Usage

``````var Pareto1 = require( '@stdlib/math/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 parameter values.

``````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

beta.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 ~14.26
``````

#### 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 = quantile( 1.9 );
// returns NaN
``````

## Examples

``````var Pareto1 = require( '@stdlib/math/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
``````