Extends the class DiscreteDistributionInt for the discrete uniform distribution over the range \([i,j]\). More...

Inheritance diagram for UniformIntDist:

Collaboration diagram for UniformIntDist:

Public Member Functions
	UniformIntDist (int i, int j)
	Constructs a discrete uniform distribution over the interval \([i,j]\).

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.

int	getI ()
	Returns the parameter \(i\).

int	getJ ()
	Returns the parameter \(j\).

void	setParams (int i, int j)
	Sets the parameters \(i\) and \(j\) for this object.

double []	getParams ()
	Return a table containing the parameters of the current distribution. More...

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 (int i, int j, int x)
	Computes the discrete uniform probability \(p(x)\) defined in ( fmassuniformint ).

static double	cdf (int i, int j, int x)
	Computes the discrete uniform distribution function defined in ( cdfuniformint ).

static double	barF (int i, int j, int x)
	Computes the discrete uniform complementary distribution function \(\bar{F}(x)\). More...

static int	inverseF (int i, int j, double u)
	Computes the inverse of the discrete uniform distribution function ( invuniformint ).

static double []	getMLE (int[] x, int n)
	Estimates the parameters \((i, j)\) of the uniform distribution over integers using the maximum likelihood method, from the \(n\) observations \(x[k]\), \(k = 0, 1, …, n-1\). More...

static UniformIntDist	getInstanceFromMLE (int[] x, int n)
	Creates a new instance of a discrete uniform distribution over integers with parameters \(i\) and \(j\) estimated using the maximum likelihood method based on the \(n\) observations \(x[k]\), \(k = 0, 1, …, n-1\). More...

static double	getMean (int i, int j)
	Computes and returns the mean \(E[X] = (i + j)/2\) of the discrete uniform distribution. More...

static double	getVariance (int i, int j)
	Computes and returns the variance \(\mbox{Var}[X] = [(j - i + 1)^2 - 1]/{12}\) of the discrete uniform distribution. More...

static double	getStandardDeviation (int i, int j)
	Computes and returns the standard deviation of the discrete uniform distribution. More...

Protected Attributes
int	i

int	j

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

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...

Static Protected Attributes inherited from DiscreteDistributionInt
static final double	EPS_EXTRA = 1.0e-6

Detailed Description

Extends the class DiscreteDistributionInt for the discrete uniform distribution over the range \([i,j]\).

Its mass function is given by

\[ p(x) = \frac{1}{j - i + 1} \qquad\mbox{ for } x = i, i + 1, …, j \tag{fmassuniformint} \]

and 0 elsewhere. The distribution function is

\[ F(x) = \left\{\begin{array}{ll} 0, & \mbox{ for } x < i \\ \displaystyle\frac{\lfloor x\rfloor-i+1}{j-i+1}, & \mbox{ for } i\le x < j \\ 1, & \mbox{ for } x \ge j. \end{array}\right. \tag{cdfuniformint} \]

and its inverse is

\[ F^{-1}(u) = i + \lfloor(j - i + 1)u\rfloor\qquad\mbox{for }0 \le u \le1. \tag{invuniformint} \]

Member Function Documentation

◆ barF()

static double barF	(	int	i,
		int	j,
		int	x
	)

static

Computes the discrete uniform complementary distribution function \(\bar{F}(x)\).

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

◆ getInstanceFromMLE()

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

static

Creates a new instance of a discrete uniform distribution over integers with parameters \(i\) and \(j\) estimated using the maximum likelihood method based on the \(n\) observations \(x[k]\), \(k = 0, 1, …, n-1\).

Parameters

x	the list of observations to use to evaluate parameters
n	the number of observations to use to evaluate parameters

◆ getMean()

static double getMean	(	int	i,
		int	j
	)

static

Computes and returns the mean \(E[X] = (i + j)/2\) of the discrete uniform distribution.

Returns: the mean of the discrete uniform distribution

◆ getMLE()

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

static

Estimates the parameters \((i, j)\) of the uniform distribution over integers using the maximum likelihood method, from the \(n\) observations \(x[k]\), \(k = 0, 1, …, n-1\).

The estimates are returned in a two-element array, in regular order: [ \(i\), \(j\)]. The maximum likelihood estimators are the values \((\hat{\imath}\), \(\hat{\jmath})\) that satisfy the equations

\begin{align*} \hat{\imath} & = \mbox{min} \{x_k\} \\ \hat{\jmath} & = \mbox{max} \{x_k\} \end{align*}

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

Parameters

x	the list of observations used to evaluate parameters
n	the number of observations used to evaluate parameters

Returns: returns the parameters [ \(\hat{\imath}\), \(\hat{\jmath}\)]

◆ getParams()

double [] getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [ \(i\), \(j\)].

Implements Distribution.

◆ getStandardDeviation()

static double getStandardDeviation	(	int	i,
		int	j
	)

static

Computes and returns the standard deviation of the discrete uniform distribution.

Returns: the standard deviation of the discrete uniform distribution

◆ getVariance()

static double getVariance	(	int	i,
		int	j
	)

static

Computes and returns the variance \(\mbox{Var}[X] = [(j - i + 1)^2 - 1]/{12}\) of the discrete uniform distribution.

Returns: the variance of the discrete uniform distribution

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

UniformIntDist.java

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ barF()

◆ getInstanceFromMLE()

◆ getMean()

◆ getMLE()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()