SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class PiecewiseLinearEmpiricalDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.PiecewiseLinearEmpiricalDist
```
All Implemented Interfaces:
Distribution

`public class PiecewiseLinearEmpiricalDistextends ContinuousDistribution`

Extends the class `ContinuousDistribution` for a piecewise-linear approximation of the empirical distribution function, based on the observations X(1),..., X(n) (sorted by increasing order), and defined as follows (e.g.,). The distribution function starts at X(1) and climbs linearly by 1/(n - 1) between any two successive observations. The density is

f (x) = 1/[(n - 1)(X(i+1) - X(i))] for X(i) <= x < X(i+1) and i = 1, 2,..., n - 1.

The distribution function is

 F(x) = 0 for x < X(1), F(x) = (i - 1)/(n - 1) + (x - X(i))/[(n - 1)(X(i+1) - X(i))] for X(i) <= x < X(i+1), F(x) = 1 elsewhere,

whose inverse is

F-1(u) = X(i) + ((n - 1)u - i + 1)(X(i+1) - X(i))

for (i - 1)/(n - 1) <= u <= i/(n - 1) and i = 1,..., n - 1.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`decPrec`

Constructor Summary
`PiecewiseLinearEmpiricalDist(double[] obs)`
Constructs a new piecewise-linear distribution using all the observations stored in obs.
`PiecewiseLinearEmpiricalDist(Reader in)`
Constructs a new empirical distribution using the observations read from the reader in.

Method Summary
` double` `barF(double x)`
Returns the complementary distribution function.
` double` `cdf(double x)`
Returns the distribution function F(x).
` double` `density(double x)`
Returns f (x), the density evaluated at x.
` double` `getMean()`
Returns the mean.
` int` `getN()`
Returns n, the number of observations.
` double` `getObs(int i)`
Returns the value of X(i).
` double[]` `getParams()`
Return a table containing parameters of the current distribution.
` double` `getSampleMean()`
Returns the sample mean of the observations.
` double` `getSampleStandardDeviation()`
Returns the sample standard deviation of the observations.
` double` `getSampleVariance()`
Returns the sample variance of the observations.
` double` `getStandardDeviation()`
Returns the standard deviation.
` double` `getVariance()`
Returns the variance.
` double` `inverseF(double u)`
Returns the inverse distribution function x = F-1(u).
` String` `toString()`
Returns a String containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### PiecewiseLinearEmpiricalDist

`public PiecewiseLinearEmpiricalDist(double[] obs)`
Constructs a new piecewise-linear distribution using all the observations stored in obs. These observations are copied into an internal array and then sorted.

### PiecewiseLinearEmpiricalDist

```public PiecewiseLinearEmpiricalDist(Reader in)
throws IOException```
Constructs a new empirical distribution using the observations read from the reader in. This constructor will read the first double of each line in the stream. Any line that does not start with a +, -, or a decimal digit, is ignored. The file is read until its end. One must be careful about lines starting with a blank. This format is the same as in UNURAN.

Throws:
`IOException`
Method Detail

### density

`public double density(double x)`
Description copied from class: `ContinuousDistribution`
Returns f (x), the density evaluated at x.

Specified by:
`density` in class `ContinuousDistribution`
Parameters:
`x` - value at which the density is evaluated
Returns:
density function evaluated at x

### cdf

`public double cdf(double x)`
Description copied from interface: `Distribution`
Returns the distribution function F(x).

Parameters:
`x` - value at which the distribution function is evaluated
Returns:
distribution function evaluated at x

### barF

`public double barF(double x)`
Description copied from class: `ContinuousDistribution`
Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:
`barF` in interface `Distribution`
Overrides:
`barF` in class `ContinuousDistribution`
Parameters:
`x` - value at which the complementary distribution function is evaluated
Returns:
complementary distribution function evaluated at x

### inverseF

`public double inverseF(double u)`
Description copied from class: `ContinuousDistribution`
Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].

Specified by:
`inverseF` in interface `Distribution`
Overrides:
`inverseF` in class `ContinuousDistribution`
Parameters:
`u` - value at which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

### getMean

`public double getMean()`
Description copied from class: `ContinuousDistribution`
Returns the mean.

Specified by:
`getMean` in interface `Distribution`
Overrides:
`getMean` in class `ContinuousDistribution`
Returns:
the mean

### getVariance

`public double getVariance()`
Description copied from class: `ContinuousDistribution`
Returns the variance.

Specified by:
`getVariance` in interface `Distribution`
Overrides:
`getVariance` in class `ContinuousDistribution`
Returns:
the variance

### getStandardDeviation

`public double getStandardDeviation()`
Description copied from class: `ContinuousDistribution`
Returns the standard deviation.

Specified by:
`getStandardDeviation` in interface `Distribution`
Overrides:
`getStandardDeviation` in class `ContinuousDistribution`
Returns:
the standard deviation

### getN

`public int getN()`
Returns n, the number of observations.

### getObs

`public double getObs(int i)`
Returns the value of X(i).

### getSampleMean

`public double getSampleMean()`
Returns the sample mean of the observations.

### getSampleVariance

`public double getSampleVariance()`
Returns the sample variance of the observations.

### getSampleStandardDeviation

`public double getSampleStandardDeviation()`
Returns the sample standard deviation of the observations.

### getParams

`public double[] getParams()`
Return a table containing parameters of the current distribution.

### toString

`public String toString()`
Returns a String containing information about the current distribution.

Overrides:
`toString` in class `Object`

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.