Overview | Package | Class | Tree | Deprecated | Index | Help
| SSJ V. 2.1.1.
PREV CLASS NEXT CLASS | FRAMES NO FRAMES
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD

## 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 PiecewiseLinearEmpiricalDist

extends 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)` Computes and returns the inverse distribution function x = F-1(u), by calling the method `inverseBrent`.
`String` | `toString()` Returns a `String` containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`inverseBisection, inverseBrent`

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), which is not accurate when F(x) -> 1.

  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`
  Computes and returns the inverse distribution function x = F-1(u), by calling the method `inverseBrent`. 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`

Overview | Package | Class | Tree | Deprecated | Index | Help
| SSJ V. 2.1.1.
PREV CLASS NEXT CLASS | FRAMES NO FRAMES
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD

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