umontreal.ssj.probdist.StudentDistQuick Class Reference

Extends the class StudentDist for the Student. More...

Inheritance diagram for umontreal.ssj.probdist.StudentDistQuick:

Public Member Functions
	StudentDistQuick (int n)
	Constructs a StudentDistQuick object with n degrees of freedom.
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
Public Member Functions inherited from umontreal.ssj.probdist.StudentDist
	StudentDist (int n)
	Constructs a StudentDist object with n degrees of freedom.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
int	getN ()
	Returns the parameter \(n\) associated with this object.
void	setN (int n)
	Sets the parameter \(n\) associated with this object.
double[]	getParams ()
	Return a table containing the parameter of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	cdf (int n, double x)
	Returns the approximation of [101]  (page 96) of the Student \(t\)-distribution function with \(n\) degrees of freedom.
static double	barF (int n, double x)
	Computes the complementary distribution function \(\bar{F}(x)\).
static double	inverseF (int n, double u)
	Returns an approximation of \(F^{-1}(u)\), where \(F\) is the Student \(t\)-distribution function with \(n\) degrees of freedom.
Static Public Member Functions inherited from umontreal.ssj.probdist.StudentDist
static double	density (int n, double x)
	Computes the density function ( fstudent ) of a Student \(t\)-distribution with \(n\) degrees of freedom.
static double	cdf2 (int n, int d, double x)
	Same as cdf(n, x).
static double[]	getMLE (double[] x, int m)
	Estimates the parameter \(n\) of the Student \(t\)-distribution using the maximum likelihood method, from the \(m\) observations.
static StudentDist	getInstanceFromMLE (double[] x, int m)
	Creates a new instance of a Student \(t\)-distribution with parameter \(n\) estimated using the maximum likelihood method based on the \(m\) observations \(x[i]\), \(i = 0, 1, …, m-1\).
static double	getMean (int n)
	Returns the mean \(E[X] = 0\) of the Student \(t\)-distribution with parameter \(n\).
static double	getVariance (int n)
	Computes and returns the variance \(\mbox{Var}[X] = n/(n - 2)\) of the Student \(t\)-distribution with parameter \(n\).
static double	getStandardDeviation (int n)
	Computes and returns the standard deviation of the Student.

Detailed Description

Extends the class StudentDist for the Student.

\(t\)-distribution. Uses methods that are faster but less precise than StudentDist.

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Definition at line 40 of file StudentDistQuick.java.

Constructor & Destructor Documentation

StudentDistQuick()

umontreal.ssj.probdist.StudentDistQuick.StudentDistQuick

(

int

n

)

Constructs a StudentDistQuick object with n degrees of freedom.

Definition at line 49 of file StudentDistQuick.java.

Member Function Documentation

barF() [1/2]

double umontreal.ssj.probdist.StudentDistQuick.barF

(

double

x

)

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns

complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.StudentDist.

Definition at line 62 of file StudentDistQuick.java.

barF() [2/2]

double umontreal.ssj.probdist.StudentDistQuick.barF ( int n, double x )

static

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

Reimplemented from umontreal.ssj.probdist.StudentDist.

Definition at line 152 of file StudentDistQuick.java.

cdf() [1/2]

double umontreal.ssj.probdist.StudentDistQuick.cdf

(

double

x

)

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns

distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.StudentDist.

Definition at line 58 of file StudentDistQuick.java.

cdf() [2/2]

double umontreal.ssj.probdist.StudentDistQuick.cdf ( int n, double x )

static

Returns the approximation of [101]  (page 96) of the Student \(t\)-distribution function with \(n\) degrees of freedom.

Is very poor in the tails but good in the central part of the range.

Reimplemented from umontreal.ssj.probdist.StudentDist.

Definition at line 75 of file StudentDistQuick.java.

inverseF() [1/2]

double umontreal.ssj.probdist.StudentDistQuick.inverseF

(

double

u

)

Returns the inverse distribution function \(x = F^{-1}(u)\).

Restrictions: \(u \in[0,1]\).

Parameters

u	value at which the inverse distribution function is evaluated

Returns

the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException

if \(u\) is not in the interval \([0,1]\)

Reimplemented from umontreal.ssj.probdist.StudentDist.

Definition at line 66 of file StudentDistQuick.java.

inverseF() [2/2]

double umontreal.ssj.probdist.StudentDistQuick.inverseF ( int n, double u )

static

Returns an approximation of \(F^{-1}(u)\), where \(F\) is the Student \(t\)-distribution function with \(n\) degrees of freedom.

Gives at least 5 decimal digits of precision when \(n \ge3\) (see [tHIL70a] ). Uses exact formulae for

\(n=1\) and \(n=2\).

Reimplemented from umontreal.ssj.probdist.StudentDist.

Definition at line 166 of file StudentDistQuick.java.

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

• src/main/java/umontreal/ssj/probdist/StudentDistQuick.java