# Logistic

Logistic distribution constructor.

## Usage

``````var Logistic = require( '@stdlib/math/base/dists/logistic/ctor' );
``````

#### Logistic( [mu, s] )

Returns a logistic distribution object.

``````var logistic = new Logistic();

var mu = logistic.mean;
// returns 0.0
``````

By default, `mu = 0.0` and `s = 1.0`. To create a distribution having a different `mu` (location parameter) and `s` (scale parameter), provide parameter values.

``````var logistic = new Logistic( 2.0, 4.0 );

var mu = logistic.mean;
// returns 2.0
``````

## logistic

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

### Writable Properties

#### logistic.mu

Location parameter of the distribution.

``````var logistic = new Logistic();

var mu = logistic.mu;
// returns 0.0

logistic.mu = 3.0;

mu = logistic.mu;
// returns 3.0
``````

#### logistic.s

Scale parameter of the distribution. `s` must be a positive number.

``````var logistic = new Logistic( 2.0, 4.0 );

var s = logistic.s;
// returns 4.0

logistic.s = 3.0;

s = logistic.s;
// returns 3.0
``````

### Computed Properties

#### Logistic.prototype.entropy

Returns the differential entropy.

``````var logistic = new Logistic( 4.0, 12.0 );

var entropy = logistic.entropy;
// returns ~4.485
``````

#### Logistic.prototype.kurtosis

Returns the excess kurtosis.

``````var logistic = new Logistic( 4.0, 12.0 );

var kurtosis = logistic.kurtosis;
// returns 1.2
``````

#### Logistic.prototype.mean

Returns the expected value.

``````var logistic = new Logistic( 4.0, 12.0 );

var mu = logistic.mean;
// returns 4.0
``````

#### Logistic.prototype.median

Returns the median.

``````var logistic = new Logistic( 4.0, 12.0 );

var median = logistic.median;
// returns 4.0
``````

#### Logistic.prototype.mode

Returns the mode.

``````var logistic = new Logistic( 4.0, 12.0 );

var mode = logistic.mode;
// returns 4.0
``````

#### Logistic.prototype.skewness

Returns the skewness.

``````var logistic = new Logistic( 4.0, 12.0 );

var skewness = logistic.skewness;
// returns 0.0
``````

#### Logistic.prototype.stdev

Returns the standard deviation.

``````var logistic = new Logistic( 4.0, 12.0 );

var s = logistic.stdev;
// returns ~21.766
``````

#### Logistic.prototype.variance

Returns the variance.

``````var logistic = new Logistic( 4.0, 12.0 );

var s2 = logistic.variance;
// returns ~473.741
``````

### Methods

#### Logistic.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

``````var logistic = new Logistic( 2.0, 4.0 );

var y = logistic.cdf( 0.5 );
// returns ~0.407
``````

#### Logistic.prototype.logcdf( x )

Evaluates the natural logarithm of the cumulative distribution function (CDF).

``````var logistic = new Logistic( 2.0, 4.0 );

var y = logistic.logcdf( 2.0 );
// returns ~-0.693
``````

#### Logistic.prototype.logpdf( x )

Evaluates the natural logarithm of the probability density function (PDF).

``````var logistic = new Logistic( 2.0, 4.0 );

var y = logistic.logpdf( 0.8 );
// returns ~-2.795
``````

#### Logistic.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

``````var logistic = new Logistic( 2.0, 4.0 );

var y = logistic.mgf( 0.2 );
// returns ~6.379
``````

#### Logistic.prototype.pdf( x )

Evaluates the probability density function (PDF).

``````var logistic = new Logistic( 2.0, 4.0 );

var y = logistic.pdf( 2.0 );
// returns 0.0625
``````

#### Logistic.prototype.quantile( p )

Evaluates the quantile function at probability `p`.

``````var logistic = new Logistic( 2.0, 4.0 );

var y = logistic.quantile( 0.5 );
// returns 2.0

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

## Examples

``````var Logistic = require( '@stdlib/math/base/dists/logistic/ctor' );

var logistic = new Logistic( 2.0, 4.0 );

var mean = logistic.mean;
// returns 2.0

var median = logistic.median;
// returns 2.0

var s2 = logistic.variance;
// returns ~52.638

var y = logistic.cdf( 0.8 );
// returns ~0.426
``````