LogarithmicDist (Java Libraries for Stochastic Simulation)

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

All Implemented Interfaces:

Distribution
```
public class LogarithmicDist
extends DiscreteDistributionInt
```
Extends the class DiscreteDistributionInt for the logarithmic distribution. It has shape parameter θ, where 0 < θ < 1. Its mass function is

p(x) = - θ^x/(x log(1 - θ) for x = 1, 2, 3,...
Its distribution function is

F(x) = -1/log(1-θ)∑_i=1^xθⁱ/i, & for x > 0.

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

Constructor Summary

Constructors
Constructor and Description

LogarithmicDist(double theta)
Constructs a logarithmic distribution with parameter θ = theta.

Constructors
Constructor and Description
`LogarithmicDist(double theta)` Constructs a logarithmic distribution with parameter θ = `theta`.

Method Summary

Methods
Modifier and Type	Method and Description
`static double`	`barF(double theta, int x)` Computes the complementary distribution function.
`double`	`barF(int x)` Returns bar(F)(x), the complementary distribution function.
`static double`	`cdf(double theta, int x)` Computes the distribution function F(x).
`double`	`cdf(int x)` Returns the distribution function F evaluated at `x` (see).
`static LogarithmicDist`	`getInstanceFromMLE(int[] x, int n)` Creates a new instance of a logarithmic distribution with parameter θ 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 theta)` Computes and returns the mean of the logarithmic distribution with parameter θ = `theta`.
`static double[]`	`getMLE(int[] x, int n)` Estimates the parameter θ of the logarithmic distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
`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 theta)` Computes and returns the standard deviation of the logarithmic distribution with parameter θ = `theta`.
`double`	`getTheta()` Returns the θ associated with this object.
`double`	`getVariance()` Returns the variance of the distribution function.
`static double`	`getVariance(double theta)` Computes and returns the variance of the logarithmic distribution with parameter θ = `theta`.
`static int`	`inverseF(double theta, double u)`
`int`	`inverseFInt(double u)` Returns the inverse distribution function F^-1(u), where 0 <= u <= 1.
`static double`	`prob(double theta, int x)` Computes the logarithmic 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`	`setTheta(double theta)` Sets the θ 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
  - LogarithmicDist
```
public LogarithmicDist(double theta)
```
    Constructs a logarithmic distribution with parameter θ = theta.
- 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 theta,
          int x)
```
    Computes the logarithmic probability p(x).
  - cdf
```
public static double cdf(double theta,
         int x)
```
    Computes the distribution function F(x).
  - barF
```
public static double barF(double theta,
          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 theta,
           double u)
```
  - getMLE
```
public static double[] getMLE(int[] x,
              int n)
```
    Estimates the parameter θ of the logarithmic 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(&thetas;)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(int[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - getInstanceFromMLE
```
public static LogarithmicDist getInstanceFromMLE(int[] x,
                                 int n)
```
    Creates a new instance of a logarithmic distribution with parameter θ 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 theta)
```
    Computes and returns the mean of the logarithmic distribution with parameter θ = theta.
    
    Returns:
    the mean of the logarithmic distribution E[X] = - θ/((1 - θ)ln(1 - θ))
  - getVariance
```
public static double getVariance(double theta)
```
    Computes and returns the variance of the logarithmic distribution with parameter θ = theta.
    
    Returns:
    the variance of the logarithmic distribution Var[X] = - θ(θ + ln(1 - θ))/((1 - θ)²(ln(1 - θ))²)
  - getStandardDeviation
```
public static double getStandardDeviation(double theta)
```
    Computes and returns the standard deviation of the logarithmic distribution with parameter θ = theta.
    
    Returns:
    the standard deviation of the logarithmic distribution
  - getTheta
```
public double getTheta()
```
    Returns the θ associated with this object.
  - setTheta
```
public void setTheta(double theta)
```
    Sets the θ 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 LogarithmicDist

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

LogarithmicDist

Method Detail

prob

cdf

barF

inverseFInt

getMean

getVariance

getStandardDeviation

prob

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getTheta

setTheta

getParams

toString