Package jline.api.pfqn.nc

Class Pfqn_nre

java.lang.Object

jline.api.pfqn.nc.Pfqn_nre

public final class Pfqn_nre
extends Object

Normalizing constant via the saddle-tilted Edgeworth (NRE) approximation. Two corrections are applied over Pfqn_nrl and Pfqn_nrp: the integrand is invariant under t -> t + c*1, so the redundant direction is quotiented out and the integral is (R-1)-dimensional; and the contour radii are tilted per class to the saddle point, making the origin a stationary point of the phase. A second-order Edgeworth term built from the third and fourth cumulants of the tilted distribution then gives a relative error of O(1/sum(N)^2). Every integrand evaluation is at real positive demands, so unlike Pfqn_nrl and Pfqn_nrp no complex arithmetic is involved.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_nre.Result	MATLAB's [lG,G,lGs,vsad]: the constant, the saddlepoint term on its own and the tilt the expansion was taken about.

Method Summary

Modifier and Type	Method	Description
static double	pfqn_nre(Matrix Lin, Matrix N, Matrix Z, Matrix alphaIn, SolverOptions options)	Logarithm of the normalizing constant of a limited load-dependent model.
static Pfqn_nre.Result	pfqn_nre_full(Matrix Lin, Matrix N, Matrix Z, Matrix alphaIn, SolverOptions options, Matrix vfix)	The full form of the reference's four outputs, named alike in the native python and C++ ports: the constant, the saddlepoint term alone and the tilt used.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

pfqn_nre

public static double pfqn_nre(Matrix Lin,
 Matrix N,
 Matrix Z,
 Matrix alphaIn,
 SolverOptions options)

Logarithm of the normalizing constant of a limited load-dependent model.

Parameters:

Lin - service demand matrix (MxR)

N - population vector (1xR)

Z - think time vector (1xR or DxR)

alphaIn - load-dependent rate matrix (Mx sum(N))

options - solver options

Returns:

logarithm of the normalizing constant

pfqn_nre_full

public static Pfqn_nre.Result pfqn_nre_full(Matrix Lin,
 Matrix N,
 Matrix Z,
 Matrix alphaIn,
 SolverOptions options,
 Matrix vfix)

The full form of the reference's four outputs, named alike in the native python and C++ ports: the constant, the saddlepoint term alone and the tilt used.

Parameters:

Lin - service demand matrix (MxR)

N - population vector (1xR)

Z - think time vector (1xR or DxR)

alphaIn - load-dependent rate matrix (Mx sum(N))

options - solver options

vfix - tilt to use instead of solving the saddle-point equation, null for the standard estimator. Supplying the tilt obtained at a nearby population makes numerator and denominator of a ratio share one expansion point, which is the Tierney-Kadane arrangement.

Returns:

the constant, the saddlepoint term and the tilt