GeometricDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
- - umontreal.iro.lecuyer.probdist.GeometricDist

All Implemented Interfaces:

Distribution
```
public class GeometricDist
extends DiscreteDistributionInt
```
Extends the class DiscreteDistributionInt for the geometric distribution with parameter p, where 0 < p < 1. Its mass function is

p(x) = p (1 - p)^x,        for x = 0, 1, 2,…
The distribution function is given by

F(x) = 1 - (1 - p)^x+1,        for x = 0, 1, 2,…
and its inverse is

F^-1(u) = floor(ln(1 - u)/ln(1 - p)),        for 0 <= u < 1.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
  EPSILON

Constructor Summary

Constructors
Constructor and Description

GeometricDist(double p)
Constructs a geometric distribution with parameter p.

Constructors
Constructor and Description
`GeometricDist(double p)` Constructs a geometric distribution with parameter p.

Method Summary

Methods
Modifier and Type	Method and Description
`static double`	`barF(double p, int x)` Computes the complementary distribution function.
`double`	`barF(int x)` Returns bar(F)(x), the complementary distribution function.
`static double`	`cdf(double p, int x)` Computes the distribution function F(x).
`double`	`cdf(int x)` Returns the distribution function F evaluated at `x` (see).
`static GeometricDist`	`getInstanceFromMLE(int[] x, int n)` Creates a new instance of a geometric distribution with parameter p estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
`static double[]`	`getMaximumLikelihoodEstimate(int[] x, int n)` Deprecated.
`double`	`getMean()` Returns the mean of the distribution function.
`static double`	`getMean(double p)` Computes and returns the mean E[X] = (1 - p)/p of the geometric distribution with parameter p.
`static double[]`	`getMLE(int[] x, int n)` Estimates the parameter p of the geometric distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
`double`	`getP()` Returns the p associated with this object.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation of the distribution function.
`static double`	`getStandardDeviation(double p)` Computes and returns the standard deviation of the geometric distribution with parameter p.
`double`	`getVariance()` Returns the variance of the distribution function.
`static double`	`getVariance(double p)` Computes and returns the variance Var[X] = (1 - p)/p² of the geometric distribution with parameter p.
`static int`	`inverseF(double p, double u)` Computes the inverse of the geometric distribution.
`int`	`inverseFInt(double u)` Returns the inverse distribution function F^-1(u), where 0 <= u <= 1.
`static double`	`prob(double p, int x)` Computes the geometric probability p(x).
`double`	`prob(int x)` Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
`void`	`setP(double p)` Resets the value of p associated with this object.
`java.lang.String`	`toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
barF, cdf, getXinf, getXsup, inverseF

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

- Constructor Detail
  - GeometricDist
```
public GeometricDist(double p)
```
    Constructs a geometric distribution with parameter p.
- Method Detail
  - prob
```
public double prob(int x)
```
    Description copied from class: DiscreteDistributionInt
    
    Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
    
    Specified by:
    
    prob in class DiscreteDistributionInt
    
    Parameters:
    x - value at which the mass function must be evaluated
    
    Returns:
    the mass function evaluated at x
  - cdf
```
public double cdf(int x)
```
    Description copied from class: DiscreteDistributionInt
    
    Returns the distribution function F evaluated at x (see).
    
    Specified by:
    
    cdf in class DiscreteDistributionInt
    
    Parameters:
    x - value at which the distribution function must be evaluated
    
    Returns:
    the distribution function evaluated at x
  - barF
```
public double barF(int x)
```
    Description copied from class: DiscreteDistributionInt
    
    Returns bar(F)(x), the complementary distribution function. See the WARNING above.
    
    Overrides:
    
    barF in class DiscreteDistributionInt
    
    Parameters:
    x - value at which the complementary distribution function must be evaluated
    
    Returns:
    the complementary distribution function evaluated at x
  - inverseFInt
```
public int inverseFInt(double u)
```
    Description copied from class: DiscreteDistributionInt
    
    Returns the inverse distribution function F^-1(u), where 0 <= u <= 1. The default implementation uses binary search.
    
    Overrides:
    
    inverseFInt in class DiscreteDistributionInt
    
    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 interface: Distribution
    
    Returns the mean of the distribution function.
  - getVariance
```
public double getVariance()
```
    Description copied from interface: Distribution
    
    Returns the variance of the distribution function.
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from interface: Distribution
    
    Returns the standard deviation of the distribution function.
  - prob
```
public static double prob(double p,
          int x)
```
    Computes the geometric probability p(x).
  - cdf
```
public static double cdf(double p,
         int x)
```
    Computes the distribution function F(x).
  - barF
```
public static double barF(double p,
          int x)
```
    Computes the complementary distribution function. WARNING: The complementary distribution function is defined as bar(F)(x) = P[X >= x].
  - inverseF
```
public static int inverseF(double p,
           double u)
```
    Computes the inverse of the geometric distribution.
  - getMLE
```
public static double[] getMLE(int[] x,
              int n)
```
    Estimates the parameter p of the geometric distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimate is returned in element 0 of the returned array.
    
    Parameters:
    x - the list of observations used to evaluate parameters
    n - the number of observations used to evaluate parameters
    
    Returns:
    returns the parameter [hat(p)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(int[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - getInstanceFromMLE
```
public static GeometricDist getInstanceFromMLE(int[] x,
                               int n)
```
    Creates a new instance of a geometric distribution with parameter p estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
    
    Parameters:
    x - the list of observations to use to evaluate parameters
    n - the number of observations to use to evaluate parameters
  - getMean
```
public static double getMean(double p)
```
    Computes and returns the mean E[X] = (1 - p)/p of the geometric distribution with parameter p.
    
    Returns:
    the mean of the geometric distribution E[X] = (1 - p)/p
  - getVariance
```
public static double getVariance(double p)
```
    Computes and returns the variance Var[X] = (1 - p)/p² of the geometric distribution with parameter p.
    
    Returns:
    the variance of the Geometric distribution Var[X] = (1 - p)/p²
  - getStandardDeviation
```
public static double getStandardDeviation(double p)
```
    Computes and returns the standard deviation of the geometric distribution with parameter p.
    
    Returns:
    the standard deviation of the geometric distribution
  - getP
```
public double getP()
```
    Returns the p associated with this object.
  - setP
```
public void setP(double p)
```
    Resets the value of p associated with this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class GeometricDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

GeometricDist

Method Detail

prob

cdf

barF

inverseFInt

getMean

getVariance

getStandardDeviation

prob

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getP

setP

getParams

toString