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AG CL Interface
g01edc (prob_f)
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AG CL Interface Introduction
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▸
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Contents
1
Purpose
2
Specification
3
Description
4
References
5
Arguments
6
Error Indicators and Warnings
7
Accuracy
8
Parallelism and Performance
9
Further Comments
▸
▿
10
Example
10.1
Program Text
10.2
Program Data
10.3
Program Results
Copyright
N
AG 2024
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CL Name Style:
Short (
a00aac
)
Long (
impl_details
)
Full (
nag_info_impl_details
)
1
Purpose
g01edc
returns the probability for the lower or upper tail of the
F
or variance-ratio distribution with real degrees of freedom.
2
Specification
copy
#include <nag.h>
double
g01edc
(
Nag_TailProbability
tail
,
double
f
,
double
df1
,
double
df2
,
NagError *
fail
)
The function may be called by the names:
g01edc
,
nag_stat_prob_f
or
nag_prob_f_dist
.
3
Description
The lower tail probability for the
F
, or variance-ratio distribution, with
ν
1
and
ν
2
degrees of freedom,
P
(
F
≤
f
:
ν
1
,
ν
2
)
, is defined by:
P
(
F
≤
f
:
ν
1
,
ν
2
)
=
ν
1
ν
1
/
2
ν
2
ν
2
/
2
Γ
(
(
ν
1
+
ν
2
)
/
2
)
Γ
(
ν
1
/
2
)
Γ
(
ν
2
/
2
)
∫
0
f
F
(
ν
1
-
2
)
/
2
(
ν
1
F
+
ν
2
)
-
(
ν
1
+
ν
2
)
/
2
d
F
,
for
ν
1
,
ν
2
>
0
,
f
≥
0
.
The probability is computed by means of a transformation to a beta distribution,
P
β
(
B
≤
β
:
a
,
b
)
:
P
(
F
≤
f
:
ν
1
,
ν
2
)
=
P
β
(
B
≤
ν
1
f
ν
1
f
+
ν
2
:
ν
1
/
2
,
ν
2
/
2
)
and using a call to
g01eec
.
For very large values of both
ν
1
and
ν
2
, greater than
10
5
, a normal approximation is used. If only one of
ν
1
or
ν
2
is greater than
10
5
then a
χ
2
approximation is used, see
Abramowitz and Stegun (1972)
.
4
References
Abramowitz M and Stegun I A (1972)
Handbook of Mathematical Functions
(3rd Edition) Dover Publications
Hastings N A J and Peacock J B (1975)
Statistical Distributions
Butterworth
5
Arguments
1:
tail
–
Nag_TailProbability
Input
On entry
: indicates whether an upper or lower tail probability is required.
tail
=
Nag_LowerTail
The lower tail probability is returned, i.e.,
P
(
F
≤
f
:
ν
1
,
ν
2
)
.
tail
=
Nag_UpperTail
The upper tail probability is returned, i.e.,
P
(
F
≥
f
:
ν
1
,
ν
2
)
.
Constraint
:
tail
=
Nag_LowerTail
or
Nag_UpperTail
.
2:
f
–
double
Input
On entry
:
f
, the value of the
F
variate.
Constraint
:
f
≥
0.0
.
3:
df1
–
double
Input
On entry
: the degrees of freedom of the numerator variance,
ν
1
.
Constraint
:
df1
>
0.0
.
4:
df2
–
double
Input
On entry
: the degrees of freedom of the denominator variance,
ν
2
.
Constraint
:
df2
>
0.0
.
5:
fail
–
NagError *
Input/Output
The
N
AG error argument (see
Section 7
in the Introduction to the
N
AG Library CL Interface).
6
Error Indicators and Warnings
Note:
on any of the error conditions listed below except
fail
.
code
=
NE_PROBAB_CLOSE_TO_TAIL
g01edc
returns
0.0
.
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See
Section 3.1.2
in the Introduction to the
N
AG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument
⟨
value
⟩
had an illegal value.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
N
AG
for assistance.
See
Section 7.5
in the Introduction to the
N
AG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See
Section 8
in the Introduction to the
N
AG Library CL Interface for further information.
NE_PROBAB_CLOSE_TO_TAIL
The probability is too close to
0.0
or
1.0
.
f
is too far out into the tails for the probability to be evaluated exactly. The result tends to approach
1.0
if
f
is large, or
0.0
if
f
is small. The result returned is a good approximation to the required solution.
NE_REAL_ARG_LE
On entry,
df1
=
⟨
value
⟩
and
df2
=
⟨
value
⟩
.
Constraint:
df1
>
0.0
and
df2
>
0.0
.
NE_REAL_ARG_LT
On entry,
f
=
⟨
value
⟩
.
Constraint:
f
≥
0.0
.
7
Accuracy
The result should be accurate to five significant digits.
8
Parallelism and Performance
Background information to multithreading can be found in the
Multithreading
documentation.
g01edc
is not threaded in any implementation.
9
Further Comments
For higher accuracy
g01eec
can be used along with the transformations given in
Section 3
.
10
Example
This example reads values from, and degrees of freedom for, a number of
F
-distributions and computes the associated lower tail probabilities.
10.1
Program Text
Program Text (g01edce.c)
10.2
Program Data
Program Data (g01edce.d)
10.3
Program Results
Program Results (g01edce.r)
N
AG Library Manual, Mark 30.3
Interfaces:
FL
CL
CPP
AD
PY
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N
AG CL Interface Introduction
G01 (Stat) Chapter Contents
G01 (Stat) Chapter Introduction
g01ed:
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Copyright
N
AG 2024