NAG Library Routine Document
G01EAF returns a one or two tail probability for the standard Normal distribution, via the routine name.
|REAL (KIND=nag_wp) G01EAF
The lower tail probability for the standard Normal distribution,
is defined by:
is used, where erfc is the complementary error function, and is computed using S15ADF
. For the upper tail probability the relationship
is used and for the two tail significance level probability twice the probability obtained from the absolute value of
When the two tail confidence probability is required the relationship
is used, where erf is the error function, and is computed using S15AEF
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
- 1: TAIL – CHARACTER(1)Input
: indicates which tail the returned probability should represent.
- The lower tail probability is returned, i.e., .
- The upper tail probability is returned, i.e., .
- The two tail (significance level) probability is returned, i.e., .
- The two tail (confidence interval) probability is returned, i.e., .
, , or .
- 2: X – REAL (KIND=nag_wp)Input
On entry: , the value of the standard Normal variate.
- 3: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
If , then G01EAF returns .
|On entry,||, , or .|
Accuracy is limited by machine precision
. For detailed error analysis see
Four values of TAIL
are input and the probabilities calculated and printed.
9.1 Program Text
Program Text (g01eafe.f90)
9.2 Program Data
Program Data (g01eafe.d)
9.3 Program Results
Program Results (g01eafe.r)