Package jdistlib

Class DiscreteTailBounds

java.lang.Object

jdistlib.DiscreteTailBounds

public final class DiscreteTailBounds
extends Object

Factory methods for common caller-certified infinite-series tail bounds.

Method Summary

Modifier and Type	Method	Description
static DiscreteTailBound	afterFinitePrefix(long firstRemainder, DiscreteTailBound remainder)	Activates a remainder certificate only after a caller-verified finite prefix has been included.
static DiscreteTailBound	beforeFinitePrefix(long firstRemainder, DiscreteTailBound remainder)	Left-moving counterpart of afterFinitePrefix(long, DiscreteTailBound).
static DiscreteTailBound	constant(double upperBound)	Uses a fixed finite upper bound, which must include the first term.
static DiscreteTailBound	geometricRatio(double maximumRatio)	Geometric/ratio-test bound.
static DiscreteTailBound	leftPowerLaw(double exponent, double offset)	Left-tail integral-test bound for weights proportional to (-k + offset)^(-exponent).
static DiscreteTailBound	rightPowerLaw(double exponent, double offset)	Right-tail integral-test bound for weights proportional to (k + offset)^(-exponent).
static DiscreteTailBound	symmetricPowerLaw(double exponent, double offset)	Power-law bound suitable for either outward tail around zero.

Methods inherited from class java.lang.Object

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

Method Details

geometricRatio

public static DiscreteTailBound geometricRatio(double maximumRatio)

Geometric/ratio-test bound. The caller promises every successive omitted weight is at most maximumRatio times its predecessor.

rightPowerLaw

public static DiscreteTailBound rightPowerLaw(double exponent,
 double offset)

Right-tail integral-test bound for weights proportional to (k + offset)^(-exponent).

leftPowerLaw

public static DiscreteTailBound leftPowerLaw(double exponent,
 double offset)

Left-tail integral-test bound for weights proportional to (-k + offset)^(-exponent).

symmetricPowerLaw

public static DiscreteTailBound symmetricPowerLaw(double exponent,
 double offset)

Power-law bound suitable for either outward tail around zero.

constant

public static DiscreteTailBound constant(double upperBound)

Uses a fixed finite upper bound, which must include the first term.

afterFinitePrefix

public static DiscreteTailBound afterFinitePrefix(long firstRemainder,
 DiscreteTailBound remainder)

Activates a remainder certificate only after a caller-verified finite prefix has been included.

beforeFinitePrefix

public static DiscreteTailBound beforeFinitePrefix(long firstRemainder,
 DiscreteTailBound remainder)

Left-moving counterpart of afterFinitePrefix(long, DiscreteTailBound).