Extends the class StudentDist for the Student \(t\)-distribution. More...
Inheritance diagram for StudentDistQuick:
Collaboration diagram for StudentDistQuick:
Public Member Functions | |
| StudentDistQuick (int n) | |
Constructs a StudentDistQuick object with n degrees of freedom. | |
| double | cdf (double x) |
| Returns the distribution function \(F(x)\). More... | |
| double | barF (double x) |
| Returns \(\bar{F}(x) = 1 - F(x)\). More... | |
| double | inverseF (double u) |
| Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More... | |
 Public Member Functions inherited from StudentDist | |
| StudentDist (int n) | |
Constructs a StudentDist object with n degrees of freedom. | |
| double | density (double x) |
| double | cdf (double x) |
| Returns the distribution function \(F(x)\). More... | |
| double | barF (double x) |
| Returns \(\bar{F}(x) = 1 - F(x)\). More... | |
| double | inverseF (double u) |
| Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More... | |
| 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 | 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 ContinuousDistribution | |
| abstract double | density (double x) |
| Returns \(f(x)\), the density evaluated at \(x\). More... | |
| double | barF (double x) |
| Returns the complementary distribution function. More... | |
| double | inverseBrent (double a, double b, double u, double tol) |
| Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More... | |
| double | inverseBisection (double u) |
| Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More... | |
| double | inverseF (double u) |
| Returns the inverse distribution function \(x = F^{-1}(u)\). More... | |
| double | getMean () |
| Returns the mean. More... | |
| double | getVariance () |
| Returns the variance. More... | |
| double | getStandardDeviation () |
| Returns the standard deviation. More... | |
| double | getXinf () |
| Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
| double | getXsup () |
| Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
| void | setXinf (double xa) |
Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
| void | setXsup (double xb) |
Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
Static Public Member Functions | |
| static double | cdf (int n, double x) |
| Returns the approximation of [105] (page 96) of the Student \(t\)-distribution function with \(n\) degrees of freedom. More... | |
| 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. More... | |
| Static Public Member Functions inherited from 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 | cdf (int n, double x) |
| Computes the Student \(t\)-distribution function \(u=F(x)\) with \(n\) degrees of freedom. More... | |
| static double | cdf2 (int n, int d, double x) |
| Same as cdf(n, x). | |
| static double | barF (int n, double x) |
| Computes the complementary distribution function \(v = \bar{F}(x)\) with \(n\) degrees of freedom. More... | |
| static double | inverseF (int n, double u) |
| Returns the inverse \(x = F^{-1}(u)\) of Student \(t\)-distribution function with \(n\) degrees of freedom. More... | |
| 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 \(x[i]\), \(i = 0, 1,…, m-1\). More... | |
| 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 \(x[i]\), \(i = 0, 1, …, m-1\). More... | |
| static double | getMean (int n) |
| Returns the mean \(E[X] = 0\) of the Student \(t\)-distribution with parameter \(n\). More... | |
| static double | getVariance (int n) |
| Computes and returns the variance \(\mbox{Var}[X] = n/(n - 2)\) of the Student \(t\)-distribution with parameter \(n\). More... | |
| static double | getStandardDeviation (int n) |
| Computes and returns the standard deviation of the Student \(t\)-distribution with parameter \(n\). More... | |
Additional Inherited Members | |
| Public Attributes inherited from ContinuousDistribution | |
| int | decPrec = 15 |
| Protected Attributes inherited from StudentDist | |
| int | n |
| Protected Attributes inherited from ContinuousDistribution | |
| double | supportA = Double.NEGATIVE_INFINITY |
| double | supportB = Double.POSITIVE_INFINITY |
| Static Protected Attributes inherited from ContinuousDistribution | |
| static final double | XBIG = 100.0 |
| static final double | XBIGM = 1000.0 |
| static final double [] | EPSARRAY |
Detailed Description
Extends the class StudentDist for the Student \(t\)-distribution.
Uses methods that are faster but less precise than StudentDist.
Member Function Documentation
◆ barF()
| double barF | ( | double | x | ) |
Returns \(\bar{F}(x) = 1 - F(x)\).
- Parameters
-
x value at which the complementary distribution function is evaluated
- Returns
- complementary distribution function evaluated at
x
Implements Distribution.
◆ cdf() [1/2]
| double 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
Implements Distribution.
◆ cdf() [2/2]
|
static |
Returns the approximation of [105] (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.
◆ inverseF() [1/2]
| double inverseF | ( | double | u | ) |
Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).
- Parameters
-
u value in the interval \((0,1)\) for which the inverse distribution function is evaluated
- Returns
- the inverse distribution function evaluated at
u
Implements Distribution.
◆ inverseF() [2/2]
|
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 [86] ). Uses exact formulae for \(n=1\) and \(n=2\).
The documentation for this class was generated from the following file:
- StudentDistQuick.java
