SSJ  3.3.1
Stochastic Simulation in Java
Classes | Public Member Functions | Static Public Member Functions | List of all members

Extends the class DiscreteDistributionInt for the logarithmic distribution. More...

Inheritance diagram for LogarithmicDist:
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Collaboration diagram for LogarithmicDist:
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Public Member Functions

 LogarithmicDist (double theta)
 Constructs a logarithmic distribution with parameter \(\theta= \) theta.
 
double prob (int x)
 
double cdf (int x)
 
double barF (int x)
 
int inverseFInt (double u)
 
double getMean ()
 Returns the mean of the distribution function.
 
double getVariance ()
 Returns the variance of the distribution function.
 
double getStandardDeviation ()
 Returns the standard deviation of the distribution function.
 
double getTheta ()
 Returns the \(\theta\) associated with this object.
 
void setTheta (double theta)
 Sets the \(\theta\) associated with this object.
 
double [] getParams ()
 Return a table containing the parameters of the current distribution.
 
String toString ()
 Returns a String containing information about the current distribution.
 
- Public Member Functions inherited from DiscreteDistributionInt
abstract double prob (int x)
 Returns \(p(x)\), the probability of \(x\). More...
 
double cdf (double x)
 Returns the distribution function \(F\) evaluated at \(x\) (see ( FDistDisc )). More...
 
abstract double cdf (int x)
 Returns the distribution function \(F\) evaluated at \(x\) (see ( FDistDisc )). More...
 
double barF (double x)
 Returns \(\bar{F}(x)\), the complementary distribution function. More...
 
double barF (int x)
 Returns \(\bar{F}(x)\), the complementary distribution function. More...
 
int getXinf ()
 Returns the lower limit \(x_a\) of the support of the probability mass function. More...
 
int getXsup ()
 Returns the upper limit \(x_b\) of the support of the probability mass function. More...
 
double inverseF (double u)
 Returns the inverse distribution function \(F^{-1}(u)\), where. More...
 
int inverseFInt (double u)
 Returns the inverse distribution function \(F^{-1}(u)\), where. More...
 

Static Public Member Functions

static double prob (double theta, int x)
 Computes the logarithmic probability \(p(x)\) given in ( flogar ) .
 
static double cdf (double theta, int x)
 Computes the distribution function \(F(x)\).
 
static double barF (double theta, int x)
 Computes the complementary distribution function. More...
 
static int inverseF (double theta, double u)
 
static double [] getMLE (int[] x, int n)
 Estimates the parameter \(\theta\) of the logarithmic distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\). More...
 
static LogarithmicDist getInstanceFromMLE (int[] x, int n)
 Creates a new instance of a logarithmic distribution with parameter \(\theta\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\). More...
 
static double getMean (double theta)
 Computes and returns the mean

\[ E[X] = \frac{-\theta}{(1 - \theta)\ln(1 - \theta)} \]

of the logarithmic distribution with parameter \(\theta= \) theta. More...

 
static double getVariance (double theta)
 Computes and returns the variance

\[ \mbox{Var}[X] = \frac{-\theta(\theta+ \ln(1 - \theta))}{[(1 - \theta) \ln(1 - \theta)]^2} \]

of the logarithmic distribution with parameter \(\theta=\) theta. More...

 
static double getStandardDeviation (double theta)
 Computes and returns the standard deviation of the logarithmic distribution with parameter \(\theta= \) theta. More...
 

Additional Inherited Members

- Static Public Attributes inherited from DiscreteDistributionInt
static double EPSILON = 1.0e-16
 Environment variable that determines what probability terms can be considered as negligible when building precomputed tables for distribution and mass functions. More...
 
- Protected Attributes inherited from DiscreteDistributionInt
double cdf [] = null
 
double pdf [] = null
 
int xmin = 0
 
int xmax = 0
 
int xmed = 0
 
int supportA = Integer.MIN_VALUE
 
int supportB = Integer.MAX_VALUE
 
- Static Protected Attributes inherited from DiscreteDistributionInt
static final double EPS_EXTRA = 1.0e-6
 

Detailed Description

Extends the class DiscreteDistributionInt for the logarithmic distribution.

It has shape parameter \(\theta\), where \(0 < \theta<1\). Its mass function is

\[ p(x) = \frac{-\theta^x}{x\log(1- \theta)} \qquad\mbox{for } x = 1,2,3,…\tag{flogar} \]

Its distribution function is

\[ F(x) = \frac{-1}{\log(1 - \theta)}\sum_{i=1}^x \frac{\theta^i}{i}, \qquad\mbox{ for } x = 1, 2, 3, … \]

and is 0 for \( x\le0\).

Member Function Documentation

◆ barF()

static double barF ( double  theta,
int  x 
)
static

Computes the complementary distribution function.

WARNING: The complementary distribution function is defined as \(\bar{F}(x) = P[X \ge x]\).

◆ getInstanceFromMLE()

static LogarithmicDist getInstanceFromMLE ( int []  x,
int  n 
)
static

Creates a new instance of a logarithmic distribution with parameter \(\theta\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\).

Parameters
xthe list of observations to use to evaluate parameters
nthe number of observations to use to evaluate parameters

◆ getMean()

static double getMean ( double  theta)
static

Computes and returns the mean

\[ E[X] = \frac{-\theta}{(1 - \theta)\ln(1 - \theta)} \]

of the logarithmic distribution with parameter \(\theta= \) theta.

Returns
the mean of the logarithmic distribution \(E[X] = -\theta/ ((1 - \theta) ln(1 - \theta))\)

◆ getMLE()

static double [] getMLE ( int []  x,
int  n 
)
static

Estimates the parameter \(\theta\) 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. The maximum likelihood estimator \(\hat{\theta}\) satisfies the equation (see [56]  (page 122))

\begin{align*} \bar{x}_n = \frac{-\hat{\theta}}{(1 - \hat{\theta}) \ln(1 - \hat{\theta})} \end{align*}

where \(\bar{x}_n\) is the average of \(x[0], …, x[n-1]\).

Parameters
xthe list of observations used to evaluate parameters
nthe number of observations used to evaluate parameters
Returns
returns the parameter [ \(\hat{\theta}\)]

◆ getStandardDeviation()

static double getStandardDeviation ( double  theta)
static

Computes and returns the standard deviation of the logarithmic distribution with parameter \(\theta= \) theta.

Returns
the standard deviation of the logarithmic distribution

◆ getVariance()

static double getVariance ( double  theta)
static

Computes and returns the variance

\[ \mbox{Var}[X] = \frac{-\theta(\theta+ \ln(1 - \theta))}{[(1 - \theta) \ln(1 - \theta)]^2} \]

of the logarithmic distribution with parameter \(\theta=\) theta.

Returns
the variance of the logarithmic distribution \(\mbox{Var}[X] = -\theta(\theta+ ln(1 - \theta)) / ((1 - \theta)^2 (ln(1 - \theta))^2)\)

The documentation for this class was generated from the following file: