This class contains common parameters and methods for the Johnson system of distributions [97], [95] with shape parameters \(\gamma\) and \(\delta> 0\), location parameter. More...
Public Member Functions | |
| double | getGamma () |
| Returns the value of \(\gamma\). | |
| double | getDelta () |
| Returns the value of \(\delta\). | |
| double | getXi () |
| Returns the value of \(\xi\). | |
| double | getLambda () |
| Returns the value of \(\lambda\). | |
| double[] | getParams () |
| Return an array containing the parameters of the current distribution. | |
| String | toString () |
| Returns a String containing information about the current distribution. | |
| Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution | |
| abstract double | density (double x) |
| Returns \(f(x)\), the density evaluated at \(x\). | |
| double | barF (double x) |
| Returns the complementary distribution function. | |
| 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 | inverseF (double u) |
| Returns the inverse distribution function \(x = F^{-1}(u)\). | |
| double | getMean () |
| Returns the mean. | |
| double | getVariance () |
| Returns the variance. | |
| double | getStandardDeviation () |
| Returns the standard deviation. | |
| 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 \([x_a, x_b]\). | |
| Public Member Functions inherited from umontreal.ssj.probdist.Distribution | |
| double | cdf (double x) |
| Returns the distribution function \(F(x)\). | |
Protected Member Functions | |
| JohnsonSystem (double gamma, double delta, double xi, double lambda) | |
| Constructs a JohnsonSystem object with shape parameters. | |
| void | setParams0 (double gamma, double delta, double xi, double lambda) |
| Sets the value of the parameters \(\gamma\), \(\delta\),. | |
Detailed Description
This class contains common parameters and methods for the Johnson system of distributions [97], [95] with shape parameters \(\gamma\) and \(\delta> 0\), location parameter.
\(\xi\), and scale parameter \(\lambda>0\). Denoting \(T=(X-\xi)/\lambda\), the variable \(Z = \gamma+ \delta f(T)\) is a standard normal variable, where \(f(t)\) is one of the following transformations:
| Family | \(f(t)\) |
| \(S_L\) | \(\ln(t)\) |
| \(S_B\) | \(\ln(t / (1-t))\) |
| \(S_U\) | \(\ln(t + \sqrt{1 + t^2})\) |
Definition at line 65 of file JohnsonSystem.java.
Constructor & Destructor Documentation
◆ JohnsonSystem()
|
protected |
Constructs a JohnsonSystem object with shape parameters.
\(\gamma= \mathtt{gamma}\) and \(\delta= \mathtt{delta}\), location parameter \(\xi= \mathtt{xi}\), and scale parameter \(\lambda= \mathtt{lambda}\).
Definition at line 78 of file JohnsonSystem.java.
Member Function Documentation
◆ getDelta()
| double umontreal.ssj.probdist.JohnsonSystem.getDelta | ( | ) |
Returns the value of \(\delta\).
Definition at line 92 of file JohnsonSystem.java.
◆ getGamma()
| double umontreal.ssj.probdist.JohnsonSystem.getGamma | ( | ) |
Returns the value of \(\gamma\).
Definition at line 85 of file JohnsonSystem.java.
◆ getLambda()
| double umontreal.ssj.probdist.JohnsonSystem.getLambda | ( | ) |
Returns the value of \(\lambda\).
Definition at line 106 of file JohnsonSystem.java.
◆ getParams()
| double[] umontreal.ssj.probdist.JohnsonSystem.getParams | ( | ) |
Return an array containing the parameters of the current distribution.
This array is put in regular order: [ \(\gamma\), \(\delta\), \(\xi\), \(\lambda\)].
Implements umontreal.ssj.probdist.Distribution.
Definition at line 131 of file JohnsonSystem.java.
◆ getXi()
| double umontreal.ssj.probdist.JohnsonSystem.getXi | ( | ) |
Returns the value of \(\xi\).
Definition at line 99 of file JohnsonSystem.java.
◆ setParams0()
|
protected |
Sets the value of the parameters \(\gamma\), \(\delta\),.
\(\xi\) and \(\lambda\).
Definition at line 115 of file JohnsonSystem.java.
◆ toString()
| String umontreal.ssj.probdist.JohnsonSystem.toString | ( | ) |
Returns a String containing information about the current distribution.
Definition at line 139 of file JohnsonSystem.java.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/probdist/JohnsonSystem.java
