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. |
scan
public static double scan(int n,
double d,
int m)
- Return
P[SN(d ) >= m], where SN(d ) is the scan
statistic. It is defined as
SN(d )= sup0 <= y <= 1-dη[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
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