EmpiricalDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.DiscreteDistribution
- - umontreal.iro.lecuyer.probdist.EmpiricalDist

All Implemented Interfaces:

Distribution
```
public class EmpiricalDist
extends DiscreteDistribution
```
Extends DiscreteDistribution to an empirical distribution function, based on the observations X₍₁₎,..., X_(n) (sorted by increasing order). The distribution is uniform over the n observations, so the distribution function has a jump of 1/n at each of the n observations.

Constructor Summary

Constructors
Constructor and Description
`EmpiricalDist(double[] obs)` Constructs a new empirical distribution using all the observations stored in `obs`, and which are assumed to have been sorted in increasing numerical order.
`EmpiricalDist(java.io.Reader in)` Constructs a new empirical distribution using the observations read from the reader `in`.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns bar(F)(x) = 1 - F(x).
`double`	`cdf(double x)` Returns the distribution function F(x).
`double`	`getInterQuartileRange()` Returns the interquartile range of the observations, defined as the difference between the third and first quartiles.
`double`	`getMean()` Computes the mean E[X] = ∑_i=1ⁿp_ix_i of the distribution.
`double`	`getMedian()` Returns the n/2^th item of the sorted observations when the number of items is odd, and the mean of the n/2^th and the (n/2 + 1)^th items when the number of items is even.
`static double`	`getMedian(double[] obs, int n)` Returns the n/2^th item of the array `obs` when the number of items is odd, and the mean of the n/2^th and the (n/2 + 1)^th items when the number of items is even.
`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()` Computes the standard deviation of the distribution.
`double`	`getVariance()` Computes the variance Var[X] = ∑_i=1ⁿp_i(x_i - E[X])² of the distribution.
`double`	`inverseF(double u)` Returns the inverse distribution function F^-1(u), defined in.
`double`	`prob(int i)` Returns p_k, the probability of the k-th observation, for 0 <= k < n.
`java.lang.String`	`toString()` Returns a `String` containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistribution
getXinf, getXsup

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

- Constructor Detail
  - EmpiricalDist
```
public EmpiricalDist(double[] obs)
```
    Constructs a new empirical distribution using all the observations stored in obs, and which are assumed to have been sorted in increasing numerical order. ¹ These observations are copied into an internal array.
  - EmpiricalDist
```
public EmpiricalDist(java.io.Reader in)
              throws java.io.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. One must be careful about lines starting with a blank. This format is the same as in UNURAN. The observations read are assumed to have been sorted in increasing numerical order.
    
    Throws:
    
    java.io.IOException
- Method Detail
  - prob
```
public double prob(int i)
```
    Description copied from class: DiscreteDistribution
    
    Returns p_k, the probability of the k-th observation, for 0 <= k < n. The result should be a real number in the interval [0, 1].
    
    Overrides:
    
    prob in class DiscreteDistribution
    
    Parameters:
    i - observation number, 0 <= k < n
    
    Returns:
    the probability of observation k
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    Specified by:
    
    cdf in interface Distribution
    
    Overrides:
    
    cdf in class DiscreteDistribution
    
    Parameters:
    x - value at which the distribution function must be evaluated
    
    Returns:
    the distribution function evaluated at x
  - barF
```
public double barF(double x)
```
    Description copied from interface: Distribution
    
    Returns bar(F)(x) = 1 - F(x).
    
    Specified by:
    
    barF in interface Distribution
    
    Overrides:
    
    barF in class DiscreteDistribution
    
    Parameters:
    x - value at which the complementary distribution function must be evaluated
    
    Returns:
    the complementary distribution function evaluated at x
  - inverseF
```
public double inverseF(double u)
```
    Description copied from interface: Distribution
    
    Returns the inverse distribution function F^-1(u), defined in.
    
    Specified by:
    
    inverseF in interface Distribution
    
    Overrides:
    
    inverseF in class DiscreteDistribution
    
    Parameters:
    u - value in the interval (0, 1) for which the inverse distribution function is evaluated
    
    Returns:
    the inverse distribution function evaluated at u
  - getMean
```
public double getMean()
```
    Description copied from class: DiscreteDistribution
    
    Computes the mean E[X] = ∑_i=1ⁿp_ix_i of the distribution.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class DiscreteDistribution
  - getVariance
```
public double getVariance()
```
    Description copied from class: DiscreteDistribution
    
    Computes the variance Var[X] = ∑_i=1ⁿp_i(x_i - E[X])² of the distribution.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class DiscreteDistribution
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: DiscreteDistribution
    
    Computes the standard deviation of the distribution.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class DiscreteDistribution
  - getMedian
```
public double getMedian()
```
    Returns the n/2^th item of the sorted observations when the number of items is odd, and the mean of the n/2^th and the (n/2 + 1)^th items when the number of items is even.
  - getMedian
```
public static double getMedian(double[] obs,
               int n)
```
    Returns the n/2^th item of the array obs when the number of items is odd, and the mean of the n/2^th and the (n/2 + 1)^th items when the number of items is even. The array does not have to be sorted.
    
    Parameters:
    obs - the array of observations
    n - the number of observations
    
    Returns:
    return the median of the observations
  - 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.
  - getInterQuartileRange
```
public double getInterQuartileRange()
```
    Returns the interquartile range of the observations, defined as the difference between the third and first quartiles.
  - getParams
```
public double[] getParams()
```
    Return a table containing parameters of the current distribution.
    
    Specified by:
    
    getParams in interface Distribution
    
    Overrides:
    
    getParams in class DiscreteDistribution
  - toString
```
public java.lang.String toString()
```
    Returns a String containing information about the current distribution.
    
    Overrides:
    
    toString in class DiscreteDistribution

Class EmpiricalDist

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistribution

Methods inherited from class java.lang.Object

Constructor Detail

EmpiricalDist

EmpiricalDist

Method Detail

prob

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getMedian

getMedian

getN

getObs

getSampleMean

getSampleVariance

getSampleStandardDeviation

getInterQuartileRange

getParams

toString