umontreal.iro.lecuyer.gof
Class FBar

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

public class FBar
extends Object

WARNING: All methods in this class are deprecated, except the method scan. They now call the method barF of the appropriate class in package probdist, which use better approximations than the ones that were previously used in this class.

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. This is non-standard but we find it convenient.

For more details about the specific distributions, see the class FDist. When F(x) is very close to 1, these methods generally provide much more precise values of bar(F)(x) than using 1 - F(x) where F(x) is computed by a method from FDist.

Method Summary

static double	andersonDarling(int n, double x) Deprecated.
static double	cramerVonMises(int n, double x) Deprecated.
static double	kolmogorovSmirnov(int n, double x) Deprecated.
static double	kolmogorovSmirnovPlus(int n, double x) Deprecated.
static double	scan(int n, double d, int m) Return P[SN(d ) >= m], where SN(d ) is the scan statistic.
static double	watsonG(int n, double x) Deprecated.
static double	watsonU(int n, double x) Deprecated.

Methods inherited from class java.lang.Object

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

Method Detail

kolmogorovSmirnov

@Deprecated
public static double kolmogorovSmirnov(int n,
                                                  double x)

Deprecated.

Use KolmogorovSmirnovDistQuick.barF(n, x) instead. Returns P[D_n > x], where D_n is the Kolmogorov-Smirnov statistic.

Parameters:

n - sample size

x - Kolmogorov-Smirnov statistic

Returns:

the complementary distribution function of the statistic evaluated at x

kolmogorovSmirnovPlus

@Deprecated
public static double kolmogorovSmirnovPlus(int n,
                                                      double x)

Deprecated.

Use KolmogorovSmirnovPlusDist.barF(n, x) instead. Returns P[D_n⁺ > x], where D_n⁺ is the Kolmogorov-Smirnov+ statistic.

Parameters:

n - sample size

x - Kolmogorov-Smirnov+ statistic

Returns:

the complementary distribution function of the statistic evaluated at x

cramerVonMises

@Deprecated
public static double cramerVonMises(int n,
                                               double x)

Deprecated.

Use CramerVonMisesDist.barF(n, x) instead. Returns P[W_n² > x], where W_n² is the Cramér-von Mises statistic.

Parameters:

n - sample size

x - Cramér-von Mises statistic

Returns:

the complementary distribution function of the statistic evaluated at x

watsonU

@Deprecated
public static double watsonU(int n,
                                        double x)

Deprecated.

Use WatsonUDist.barF(n, x) instead. Returns P[U_n² > x], where U_n² is the Watson U statistic.

Parameters:

n - sample size

x - Watson U_n² statistic

Returns:

the complementary distribution function of the statistic evaluated at x

watsonG

@Deprecated
public static double watsonG(int n,
                                        double x)

Deprecated.

Use WatsonGDist.barF(n, x) instead. Returns P[G_n > x], where G_n is the Watson G statistic.

Parameters:

n - sample size

x - Watson G statistic

Returns:

the complementary distribution function of the statistic evaluated at x

andersonDarling

@Deprecated
public static double andersonDarling(int n,
                                                double x)

Deprecated.

Use AndersonDarlingDistQuick.barF(n, x) instead. Returns P[A_n² > x], where A_n² is the Anderson-Darling statistic.

Parameters:

n - sample size

x - Anderson-Darling statistic

Returns:

the complementary distribution function of the statistic evaluated at x

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