umontreal.iro.lecuyer.gof
Class FBar

java.lang.Object
  umontreal.iro.lecuyer.gof.FBar

public class FBar
extends Object

This class is similar to FDist, except that it provides static methods to compute or approximate the complementary distribution function of X, which we define as bar(F)(x) = P[X >= x], instead of F(x) = P[X <= x]. Note that with our definition of bar(F), one has bar(F)(x) = 1 - F(x) for continuous distributions and bar(F)(x) = 1 - F(x - 1) for discrete distributions over the integers.

Method Summary

static double

scan(int n, double d, int m) Return P[SN(d ) >= m], where SN(d ) is the scan statistic.

Methods inherited from class java.lang.Object

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

Method Detail

scan

public static double scan(int n,
                          double d,
                          int m)

Return P[S_N(d ) >= m], where S_N(d ) is the scan statistic. It is defined as

S_N(d )= sup_{0 <= y <= 1-d}η[y, y + d],

where d is a constant in (0, 1), η[y, y + d] is the number of observations falling inside the interval [y, y + d], from a sample of N i.i.d. U(0, 1) random variables. The approximation returned by this function is generally good when it is close to 0, but is not very reliable when it exceeds, say, 0.4. Restrictions: N >= 2 and d <= 1/2.

Parameters:

n - sample size ( >= 2)

d - length of the test interval (∈(0, 1))

m - scan statistic

Returns:

the complementary distribution function of the statistic evaluated at m