Extends the class NortaInitDisc and implements the algorithm NI1. More...
Public Member Functions | |
| NI1 (double rX, DiscreteDistributionInt dist1, DiscreteDistributionInt dist2, double tr, double tolerance) | |
| Constructor with the target rank correlation rX, the two discrete marginals dist1 and dist2, the parameter for truncation tr (see the constructor of class NortaInitDisc ) and the specific parameter \(\epsilon=\) tolerance defined above for the algorithm NI1. | |
| double | computeCorr () |
| Computes and returns the correlation \(\rho_Z\) using the algorithm NI1. | |
| Public Member Functions inherited from umontreal.ssj.probdistmulti.norta.NortaInitDisc | |
| NortaInitDisc (double rX, DiscreteDistributionInt dist1, DiscreteDistributionInt dist2, double tr) | |
| Constructor with the target rank correlation rX, the two discrete marginals dist1 and dist2 and the parameter for the truncation tr. | |
| void | computeParams () |
| Computes the following inputs of each marginal distribution: | |
| double | integ (double r) |
| Computes the function. | |
| double | deriv (double r) |
| Computes the derivative of \(g_r\), given by. | |
Detailed Description
Extends the class NortaInitDisc and implements the algorithm NI1.
It uses an algorithm based on Brent method for root-finding, which combines root-bracketing, bisection and inverse quadratic interpolation. It calls the method integ to compute the function \(g_r\) given in ( gr_M ). The search should be done in the interval \([-1,0]\) if
\(r_X\in[-1,0]\), or \([0,1]\) if \(r_X\in[0,1]\). At each iteration, the algorithm halves the interval length and uses an accuracy \(\epsilon\) to find the root \(\rho_Z\) of equation ( fr ).
Constructor & Destructor Documentation
◆ NI1()
| umontreal.ssj.probdistmulti.norta.NI1.NI1 | ( | double | rX, |
| DiscreteDistributionInt | dist1, | ||
| DiscreteDistributionInt | dist2, | ||
| double | tr, | ||
| double | tolerance ) |
Constructor with the target rank correlation rX, the two discrete marginals dist1 and dist2, the parameter for truncation tr (see the constructor of class NortaInitDisc ) and the specific parameter \(\epsilon=\) tolerance defined above for the algorithm NI1.
Member Function Documentation
◆ computeCorr()
| double umontreal.ssj.probdistmulti.norta.NI1.computeCorr | ( | ) |
Computes and returns the correlation \(\rho_Z\) using the algorithm NI1.
a, b, c, fa, fb, fc, and tolerance correspond to a, b, c, f(a) f(b), f(c) and epsilon, respectively, in the paper (paragraph "Method NI1" of section 3).
Reimplemented from umontreal.ssj.probdistmulti.norta.NortaInitDisc.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/probdistmulti/norta/NI1.java
