Package jline.api.fj

Class FJ_charmax_ext

java.lang.Object

jline.api.fj.FJ_charmax_ext

public final class FJ_charmax_ext
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	FJ_charmax_ext.DiscreteDist	The lattice laws whose characteristic maximum is closed.
static final class	FJ_charmax_ext.FJCharMaxBlomResult	[mK, lo, hi] of fj_char_max_blom; the bracket is the standard normal one.
static final class	FJ_charmax_ext.FJCharMaxDiscreteResult	[MK, mK, exact] of fj_char_max_discrete.

Method Summary

Modifier and Type	Method	Description
static FJ_charmax_ext.FJCharMaxBlomResult	fj_char_max_blom(int K)
static FJ_charmax_ext.FJCharMaxBlomResult	fj_char_max_blom(int K, DoubleUnaryOperator Finv, double alpha, double beta)	Blom-corrected plotting position for the characteristic maximum, m_K = F^-1( (K - alpha) / (K - alpha - beta + 1) ), which for alpha = beta = 0 falls back on the naive K/(K+1).
static FJ_charmax_ext.FJCharMaxDiscreteResult	fj_char_max_discrete(int K, FJ_charmax_ext.DiscreteDist dist, double par)	Gravey's characteristic maximum for a lattice law.

Methods inherited from class java.lang.Object

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

Method Details

fj_char_max_discrete

public static FJ_charmax_ext.FJCharMaxDiscreteResult fj_char_max_discrete(int K,
 FJ_charmax_ext.DiscreteDist dist,
 double par)

Gravey's characteristic maximum for a lattice law. With m_K the smallest integer at which P(X > m_K) <= 1/K, M_K = m_K + K sum_{k >= m_K} P(X > k), which upper bounds the expected maximum of K i.i.d. copies at O(1) instead of the alternating binomial sum. For the geometric the tail sum is K p^(m_K+1)/(1-p); for the Poisson it is the same sum rewritten through E[(X-m)^+] = theta P(X>m-1) - m P(X>m).

fj_char_max_blom

public static FJ_charmax_ext.FJCharMaxBlomResult fj_char_max_blom(int K,
 DoubleUnaryOperator Finv,
 double alpha,
 double beta)

Blom-corrected plotting position for the characteristic maximum, m_K = F^-1( (K - alpha) / (K - alpha - beta + 1) ), which for alpha = beta = 0 falls back on the naive K/(K+1). For the standard normal the position is bracketed for K >= 5 by sqrt(2 ln K - ln ln K - 3) < m_K < sqrt(2 ln K - ln ln K).

fj_char_max_blom

public static FJ_charmax_ext.FJCharMaxBlomResult fj_char_max_blom(int K)