NAG FL Interface
g01eaf (prob_​normal)

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1 Purpose

g01eaf returns a one or two tail probability for the standard Normal distribution.

2 Specification

Fortran Interface
Function g01eaf ( tail, x, ifail)
Real (Kind=nag_wp) :: g01eaf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x
Character (1), Intent (In) :: tail
C Header Interface
#include <nag.h>
double  g01eaf_ (const char *tail, const double *x, Integer *ifail, const Charlen length_tail)
The routine may be called by the names g01eaf or nagf_stat_prob_normal.

3 Description

The lower tail probability for the standard Normal distribution, P(Xx) is defined by:
Z(X)=12π e-X2/2, -<X< .  
The relationship
is used, where erfc is the complementary error function, and is computed using s15adf. For the upper tail probability the relationship P(Xx)=P(X-x) is used and for the two tail significance level probability twice the probability obtained from the absolute value of x is returned.
When the two tail confidence probability is required the relationship
P(X|x|)-P(X-|x|)=erf(|x|2) ,  
is used, where erf is the error function, and is computed using s15aef.

4 References

NIST Digital Library of Mathematical Functions
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

5 Arguments

1: tail Character(1) Input
On entry: indicates which tail the returned probability should represent.
The lower tail probability is returned, i.e., P(Xx).
The upper tail probability is returned, i.e., P(Xx).
The two tail (significance level) probability is returned, i.e., P(X|x|)+P(X-|x|).
The two tail (confidence interval) probability is returned, i.e., P(X|x|)-P(X-|x|).
Constraint: tail='L', 'U', 'S' or 'C'.
2: x Real (Kind=nag_wp) Input
On entry: x, the value of the standard Normal variate.
3: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
If ifail0, then g01eaf returns 0.0.
On entry, tail=value.
Constraint: tail='L', 'U', 'S' or 'C'.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Accuracy is limited by machine precision. For detailed error analysis see s15adf and s15aef.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01eaf is not threaded in any implementation.

9 Further Comments


10 Example

Four values of tail and x are input and the probabilities calculated and printed.

10.1 Program Text

Program Text (g01eafe.f90)

10.2 Program Data

Program Data (g01eafe.d)

10.3 Program Results

Program Results (g01eafe.r)